Lines and Angles - Chapter 5, Introduction - NCERT Class 7th Maths
Class: 7th
✔️ Subject: Math
✔️ Chapter: Lines & Angles
✔️ Topic Name: Introduction , Ex 5.1
✔️ Subject: Math
✔️ Chapter: Lines & Angles
✔️ Topic Name: Introduction , Ex 5.1
Category
📚
LearningTranscript
00:00Hello everyone, welcome to Insightful Maths. In today's session we are going to learn very
00:06important concept of class 7. The name of the chapter is Lines and Angles. We all are
00:12aware what are lines, what are angles. So different concepts of going ahead whatever
00:18you have already learnt in grade 6 that we will see here, we will learn here. So if you
00:23are in grade 7 and this topic is coming in your half yearly exam or you must have already
00:29learnt it in the school and you need a quick revision, this video is for you. So I request
00:35please see the video till end so that you get clarity on all the concepts which are
00:39there in this chapter. So let's begin the session. First thing that we need to know
00:45about in this chapter is this term what are complementary angles. Please mind the spelling,
00:52it is not PLI like that complement, it is not. It is complementary angles. Any two angles
00:59whose sum is 90 degree. If any two angles are given, you add their measure and the sum
01:06is 90 degree. Those pair of angles are known as complementary angles. We are talking about
01:14the pair of angles. Pair means two angles. So any two angles when you sum it up, if the
01:20sum is 90 degree, those are known as complementary angles. And each angle is known as the complement
01:28of another one. What does it mean? We can see here, these two angles are here. If I
01:34add 65 and 25, what do you get? It is 90 degree. That means these two angles are complementary
01:42angles. The question can be asked in this manner. If one of the angle is 30 degree,
01:49one of the angle is 30 degree, find the complement of this angle. Complement means if that angle
01:58is added to 30 degree, the sum should be 90 degree. Why 90? Because it is as per the definition,
02:05the sum of two complementary angles has to be 90 degree. So how do I get another angle?
02:13When one of the complementary angles is given and you are supposed to find out the other
02:17one, just subtract the given angle from 90. So unknown angle x will be equal to 90 minus
02:2630 and your answer is 60. Since we are talking about angles which are measured in degrees,
02:32you have to put this symbol of degree here. Your answer is 60 degrees. Correct? So if
02:38you know one complementary angle and you are supposed to find the complement of this angle,
02:4490 minus the given angle. It could be asked in the terms of a variable as well. If I ask you,
02:51one of the angle is x, what is the complement of this angle? So what do we do? 90 minus given
02:59angle in degrees. This is the complement of the given angle. Correct? In the similar manner,
03:06another pair of angles is supplementary angles. For complementary, the sum was 90.
03:12For supplementary, the sum has to be 180. So any pair of angles where the sum of two angles is 180,
03:22those are known as supplementary angles and each angle is known as the supplement of the other one.
03:30For example, have a look here. If I add 120 and 60, sum comes 180 degree.
03:39These are supplementary angles. It could be for example, 180. If I give you the pair of these
03:47angles and you add them up, you will again get 180 degree. So this pair of angles is again a
03:54pair of supplementary angles. If I give you one of the angles, for example, 95 degrees,
04:02and I ask you, what is the supplement of this angle? You should know that supplement means
04:09another angle which when added to 95, it should give you the sum 180 degrees.
04:16So now you calculate, what has to be added to get 180 degrees in 95?
04:22So the value of this unknown angle is 180 minus the given angle. So what is the answer?
04:30That is 85 degrees. When you minus these two, you will get your answer.
04:37If you know one angle in the supplementary angle and want to find the other one,
04:42straight away 180 minus the given angle. If for supplementary angles, one angle is known
04:48and another is required, 90 minus another angle. This much is clear?
04:54Now one of the very interesting thing or the basic thing that you should know is,
04:59what is the measure of the supplementary angle such that both the angles are equal?
05:06What is the measure of the angle for which supplementary angles both are equal?
05:12If there are two complementary angles and both are equal, what should be the sum of both?
05:17Since the angles are equal, I am taking both as x.
05:21x plus x, what is the sum? It should be 90 degrees.
05:25x plus x, what is that? That is 2x, it goes for 90 degrees.
05:31Twice of x, twice of which number is 90 degrees? Twice of which angle is 90 degrees?
05:37Twice of which number is 90 degrees? That is 45.
05:41So value of x is 90 divided by 2, that is 45 degrees.
05:47So at 45 degrees, both the complementary angles are equal to each other.
05:53In the similar manner, at which measure both the supplementary angles will be equal?
05:59What is the sum of the supplementary angles? 180.
06:02We have to split 180 into two parts so that both the angles are equal.
06:07So what should be the measure? It is 90-90 each.
06:11In complementary, at 45 degrees, both the angles are equal.
06:15For supplementary, if both the angles have to be equal,
06:18the measure of each angle has to be 90 degrees.
06:22I hope this much is understood. Let's go ahead.
06:27Another topic now, adjacent angles.
06:31Very interesting and very important thing that you need to know.
06:34What are the pair of adjacent angles? I am making a figure here, just understand this.
06:40Adjacent means you can just remember like the neighbors.
06:44Neighboring angles. For example, this is one figure.
06:49Let me make one more so that you understand that better.
06:53I have made this figure. Now let's understand what are adjacent angles.
06:58Since at this figure, angles are made using the rays, I have made the rays.
07:03Let it be the vertex O. I am marking another point on the rays so that we can name that
07:10easily and you understand what I am talking about.
07:13Let's say this is point A, point B and point C.
07:17This is point A, point B and point C.
07:22Adjacent angles means the angles which are joined together, which have one common vertex.
07:31There should be one common vertex and one common arm.
07:36And the non-common arm should be on the different sides of the common arm.
07:43For example, I talk about this is first angle which is B, O, C.
07:50Another angle is A, O, B. Second angle.
07:54Now I want to know whether these two are adjacent or not.
07:58The easiest way is to see whether these two angles are adjacent.
08:01For example, our neighbors live with us.
08:04Our houses are joined but we do not share any area in between.
08:08The inside portion of our house is different and the inside portion of their house is different.
08:13Just a common wall is there in between.
08:16In the similar manner, angle 1 and angle 2, are they having a common vertex?
08:21Both the vertices are O.
08:23This is a common vertex.
08:25This arm is O, B.
08:30Is this coming in the first angle or the second angle?
08:34Both the angles are joined on O, B.
08:37They have one common vertex and one common arm.
08:41The third point means the arms which are not common.
08:46This arm is O, C.
08:48This is the part of the first angle.
08:50The second arm is O, A.
08:52This is the part of the second angle.
08:54The arms which are not common should be on the different sides of the common arm.
09:00It is not that I put this O, A down here or O, C should come up.
09:05If one arm is up and one arm is down, it should be like this.
09:10How can you remember this differently?
09:13Both have a common vertex and a common arm.
09:17The interior portion is for angle 2.
09:25This interior portion is for angle 1.
09:28Is there any mixing of the area?
09:31There is no mixing of the area.
09:32Both the areas are different.
09:34These two are adjacent angles.
09:37They are attached to each other and still they are having different areas.
09:42The common arm should have the other two rays on its opposite side.
09:50Let us take this topic ahead.
09:52I have not talked about measurement here.
09:54Adjacent means measurement could be any.
09:57They should be attached to each other.
10:00Their area should not be the same.
10:03Now have a look at this figure.
10:05Let us understand this.
10:06Is this adjacent or not?
10:08I call this O.
10:10This point is B.
10:12This point is C.
10:14And this point is A.
10:17The distance from here to here, let me take it as 1.
10:20This distance, let me take it as 2.
10:23Now I want to know if these two are adjacent or not.
10:27First thing for adjacent angles is they should have a common vertex.
10:31Vertex is this.
10:32If I make an angle, this point where the two rays are joined together, this is the vertex.
10:39What is the vertex of the first angle?
10:41O.
10:42What is the vertex of the second angle?
10:44O.
10:46First point is verified.
10:48They have the common vertex.
10:50Second point is they should have common arm.
10:53One arm of both should be common.
10:56Look at the angle 1.
10:58One arm is OC.
10:59This is below.
11:00One arm is OB.
11:02This is above.
11:03Now in the second angle, one arm is OA.
11:07One arm is OB.
11:09Is this arm common in both the angles?
11:11These two angles, 1 and 2, these two are joined on OB.
11:15Common arm is also done.
11:17Third point is, this common arm, the other uncommon arm, which is different, which is not shared,
11:27both should be on the opposite side of this OB.
11:30Now look at the angle 2 arm.
11:32This is on the left side.
11:34Angle 1 arm is on the right side of OB.
11:38Can I say these two are adjacent angles?
11:41Answer is yes.
11:42They are adjacent.
11:47Let's say this is angle 1.
11:50This is the whole angle 1.
11:53I am making another angle in between.
11:55For example, this one.
11:58This small one is angle 2.
12:01I want to know whether these two are adjacent or not.
12:07I need to name it.
12:08This is O.
12:10This is A.
12:11This is B.
12:13And this is C.
12:23First thing, they should have a common vertex.
12:26Angle 2 vertex is O.
12:28Angle A, the vertex of the bigger angle is O.
12:31The common vertex of both is verified.
12:34Second part, they should have a common arm.
12:37One ray should be common.
12:39Second angle, look at this angle.
12:42This is the second angle.
12:44In this, one ray is OB.
12:47First angle, this red angle.
12:49In this, OA and OC.
12:51Which ray is common in both?
12:53OC.
12:53When I made this blue angle, OC is also a part of it.
12:57When I am making a big red angle, OC is also a part of it.
13:01So, ray OC is common in both.
13:04Vertex O is common in both.
13:06Two things are verified.
13:08But what does your third part say?
13:11The common arm.
13:13What is common here?
13:14OC.
13:15The other two arms which are not common.
13:18They should be on the opposite side of OC.
13:21If one is top, the other is bottom.
13:24If one is left, the other is right.
13:26Now you see, OC is below.
13:28The uncommon arm of red is also on the upper part.
13:32The blue one is also on the upper part.
13:35These two are on the same side.
13:37And there is an overlapping of area also.
13:40This blue area of angle 2.
13:43All this angle is in 1.
13:46Neighbors do not share their areas.
13:49We don't share the house.
13:51So, this pair of angles is non-adjacent.
13:55Because uncommon arms are lying on the same side of the common arm.
14:01Getting it?
14:02So, that is how these two are adjacent and the third one is non-adjacent.
14:08Let's move to the next topic now.
14:11Another term you need to know is a linear pair.
14:15Linear means...
14:15See, we pick up a word from here, line.
14:19We can remember it from here.
14:20In a linear pair, there is a word line.
14:23Angles made on a straight line are known as a linear pair.
14:28You see, we just saw this diagram.
14:30The sum of these two angles is what?
14:32This is supplementary.
14:34If one is 120 and the other is 60.
14:36I will add both of them.
14:37180.
14:37What is 180?
14:38It is supplementary.
14:40Now see one more thing.
14:42The adjacent angles we read here.
14:45This is a common vertex.
14:47Angle 60 and 120 are common.
14:49Vertex is also common.
14:51And this blue arm is also common.
14:54Both are of 60 and 120.
14:56Both have different areas.
14:58So, are these adjacent angles?
15:01Absolutely.
15:02These are adjacent angles.
15:04These are adjacent angles.
15:07Their sum is supplementary.
15:09Absolutely supplementary.
15:10The sum is 180.
15:12So, we can say that a pair of adjacent angles
15:16whose non-common arms
15:18This one is non-common.
15:20This blue one is common.
15:22This and this, they are uncommon.
15:24They should make a straight line.
15:26That is, these uncommon arms are in opposite directions.
15:31And they are making a straight line.
15:34Opposite rays.
15:35This kind of angle is known as a linear pair.
15:39Wherever we have to use angles on a straight line,
15:42we will say linear pair.
15:44What is a linear pair?
15:46It is the pair of adjacent angles whose sum is 180.
15:51The pair of angles on a straight line is 180.
15:57For example, I take this straight line.
16:00This is one of the angles.
16:03If I say, this angle is, let's say, 40 degrees.
16:11What is the value of x?
16:12I didn't say anything.
16:15Angles on a straight line, they sum up to 180 degrees.
16:26And what is the reason?
16:28The reason is linear pair.
16:31Linear pair.
16:34Angles on a straight line are linear pair.
16:38Their sum is 180.
16:40One of the 180 angles is 40 degrees.
16:42So, what is the value of the other one?
16:44It has to be 180 minus the given angle 40.
16:48Answer is 140.
16:5240 plus 140.
16:53It is giving you 180 angles on the straight line.
16:59Very good.
17:00Let us move to another one now.
17:03One of the easiest kind of angles, vertically opposite angles.
17:09We know that whenever two lines cross each other,
17:14Intersecting lines.
17:16They are intersecting.
17:18Intersecting means crossing each other at one common point.
17:29When they intersect, they are forming certain angles.
17:32For example, 1, 2, 3 and 4.
17:37Whenever two lines intersect each other,
17:41The pair of vertically opposite angles is always equal.
17:46How do we identify vertically opposite?
17:49Now, look at this.
17:50This is angle 1.
17:51We are looking for the opposite.
17:53Opposite means the one which is not connected to this.
17:561 and 2 are directly connected.
18:001 and 4 are also directly connected.
18:02So, which angle is not directly connected?
18:051 and 3.
18:07So, 1 and 3.
18:08What is this?
18:10Angle 1 is equal to angle 3.
18:13They are vertically opposite angles.
18:16In the similar manner,
18:17Angle 4 is also connected to 1 and 3.
18:21Which is not connected?
18:222.
18:23So, this angle 4 and this angle 2.
18:26They are vertically opposite and they are always equal.
18:31Now, let me ask you a question.
18:35The value of angle B is 120 degrees.
18:39Get me the values of all the angles.
18:42How do we know this?
18:43We know one angle.
18:44We should know the rest.
18:46Look at the first thing.
18:48There is a cross here.
18:49The two lines are intersecting each other.
18:52B and M are directly joined.
18:55They cannot be vertically opposite.
18:58B and M are directly joined.
19:01They cannot be.
19:02Which angle is not directly joined to B?
19:05A.
19:05Can you see?
19:06Both are in yellow.
19:08These two are vertically opposite angles.
19:11And they are always equal.
19:12So, what is the value of A directly?
19:14120 degrees.
19:16Whenever we use properties like this,
19:19you need to mention which property have you used.
19:21So, you have to mention these are vertically opposite angles.
19:25I have written the short form.
19:26You have to write the whole thing.
19:28They are vertically opposite angles.
19:30But what should we do with M and N?
19:32There is no clue given for this.
19:34What did we just read?
19:37We need to put the angles on the straight line.
19:40It will be summed up to 180 degrees.
19:43Now, look carefully.
19:44PQ is a straight line.
19:46So, angle B plus angle N.
19:49What should be the sum of both?
19:51It should be 180.
19:52What is the answer?
19:55So, if one angle is 120,
19:57what is another angle?
19:58It should be 180 minus 120.
20:02So, answer is 60 degrees.
20:04What is the value of N?
20:0660 degrees.
20:07Now, two lines are crossing.
20:09M and M.
20:11You can see in blue.
20:12They are vertically opposite.
20:14So, value of N is 60 degrees.
20:16M is also 60 degrees.
20:19It's a very interesting chapter.
20:20It is just that practice more and more questions.
20:23You will enjoy these topics.
20:25Very easy and interesting chapter.
20:27Okay.
20:27I hope vertically opposite angles is done.
20:29You have understood.
20:31Let us go ahead for another pair of angles.
20:34We have just talked about intersecting lines.
20:37Whenever two lines meet each other at one common point
20:42and they cut each other.
20:43We call such pairs of lines as intersecting lines.
20:47You know this already.
20:49Now, what is the transverse?
20:50Very important.
20:52If I have any two lines,
20:54they may be parallel.
20:56They may not be parallel.
20:57Hardly matters.
20:59If any two or more lines are there
21:02and these are intersected by a third line.
21:06Intersected means these are cut by any third line.
21:11This third line is called transversal.
21:17What is a transversal?
21:18It is a line which intersects two or more lines at different points.
21:23Very important.
21:25First line is cut here.
21:27Second line is cut here.
21:29These are different points.
21:31So, transversal is a line which intersects two or more lines at different points.
21:37This particular third line is your transversal.
21:40It is not necessary that your parallel lines will also be horizontal.
21:44Please understand.
21:45We will be able to create it.
21:49Suppose, I have these two parallel lines.
21:52This is the third line which has cut both of them.
21:55Now, what is transversal?
21:57Two lines were already there.
22:00These two.
22:01And the third line has come which is intersecting these two.
22:06Now, this line is your transversal.
22:11So, please don't get confused.
22:13Again, what is a transversal?
22:15It is a line which intersects two or more lines at different points.
22:21This line is your transversal.
22:24Now, transversal makes total how many angles if I am having two parallel lines?
22:30Red line is your transversal.
22:33It makes eight angles.
22:36And there are certain properties of these eight angles which you should know very well
22:41to do the questions based on these properties.
22:451, 2, 3, 4, 5, 6, 7, 8.
22:48When a transversal cuts or intersects two parallel lines, we get these eight angles.
22:56First, you need to know what are interior angles.
22:59Look carefully.
23:00These are also two parallel lines.
23:02One is this and one is that.
23:04These are two parallel lines.
23:05When a transversal cuts or intersects these two parallel lines,
23:12it means these two and these two.
23:16The angles between two parallel lines in the interior region are called interior angles.
23:23The angles which are not in the interior region are called outside angles.
23:27Those are exterior angles.
23:29The best way to learn it is to look at the interior angles between two parallel lines.
23:35Angle 3 is in the middle, angle 4 is in the middle, angle 5 is in the middle and angle 6 is in the middle.
23:41In this region, the angles between these two are called interior angles.
23:46The angles which are outside the line are called exterior angles.
23:51So, which all are interior here?
23:533, 4, 5, 6.
23:55I can write angle 3, angle 4, angle 5, angle 6.
24:00These are interior angles.
24:03Whenever we talk about properties, alternate, you have to remember which are the interior angles.
24:11Between two parallel lines, the angles which are not in the interior, which are outside,
24:16those are exterior.
24:17So, here exterior is 1 and 2.
24:20They are not in the middle of the parallel line.
24:22These two are outside.
24:241, 2. Likewise, 7, 8.
24:27Half and half are transferred.
24:294 are interior and 4 are exterior.
24:32How to remember?
24:33Angle between two parallel lines, these two are interior.
24:37Two up and two down are exterior.
24:41This much understood?
24:43Let's come to now corresponding angles.
24:47Another term now you should know is corresponding angles.
24:55Correspond means which have the same position.
25:00What does it mean?
25:02Here, look carefully.
25:08If I shade it here,
25:10angle 2 is above the parallel line, on the right of the transversal.
25:16What is the other angle of the same position?
25:19This is also a parallel line.
25:20Above this, on the right of the transversal.
25:23Now, look carefully.
25:25Both angles have same position.
25:27Above the line, on the right of the transversal.
25:29Above the line, on the right of the transversal.
25:31So, whenever two lines are parallel,
25:34the pair of all the corresponding angles are equal.
25:38What are the corresponding angles here?
25:40First pair, angle 2 is equal to angle 6.
25:43I hope you are able to make out.
25:46This position and this position are exactly the same.
25:50Let us see another pair of corresponding angles.
25:55Above the parallel line, on the left of the transversal.
25:58If I shade it, the green one.
26:01What is the other angle of the same position?
26:05Above the parallel line, on the left of the transversal.
26:08Look carefully.
26:09The position is exactly the same.
26:11So, I can write, angle 1 is equal to angle 5.
26:15Same position, corresponding angles.
26:18We will be able to get 4.
26:20Now, come to the next.
26:22Below the parallel line, on the right of the transversal.
26:26Below the parallel line, on the right of the transversal.
26:29So, angle 4 is equal to angle 8.
26:32So, which is now the last one?
26:34Angle 3, below the parallel line.
26:37Angle 7, below the parallel line.
26:40Angle 3 is equal to angle 7.
26:45These are the pairs of corresponding angles.
26:48Corresponding means, which are at the same position.
26:55Their position should be the same.
26:582 and 6.
27:001 and 5.
27:024 and 8.
27:033 and 7.
27:05If two lines are parallel.
27:07These corresponding pairs of angles will always be equal.
27:12If I know that angle 2 is 60 degrees.
27:15Then you can directly say.
27:17If these two lines, L and M are parallel.
27:21One is transversal.
27:22Angle 2 is 60.
27:24You will be asked, what is equal to angle 6 and Y?
27:28Angle 2 is equal to angle 6.
27:30Which is equal to 60 degrees.
27:32What is the reason?
27:33Same reason, corresponding angle.
27:36Good to go.
27:37After corresponding angles, please have a look.
27:41The pair of alternate interior angles.
27:46What are alternate interior angles?
27:52First word, the clue here is interior angles.
27:56Interior means, I told you the angles between these two parallel lines.
28:03I am talking about 3, 4, 5, 6.
28:06We are talking about these four angles.
28:09Alternate means, if one angle is on the left.
28:12The other should be on the right.
28:15One should be at the top and one should be at the bottom.
28:17Keep this in mind.
28:18Now what does it mean?
28:20Angle 3.
28:22It is an interior angle.
28:24It is at the top and at the left.
28:26At the left of the transversal, it is at the top.
28:28So angle 3 and angle 6.
28:31They are always equal if two lines are parallel.
28:34We will call them alternate interior angles.
28:39In the similar manner, angle 4 and angle 5.
28:44Angle 4 and angle 5.
28:46In opposite positions.
28:48One is at the right of the transversal and the other is at the left of the transversal.
28:52One is at the top and the other is at the bottom.
28:54I told you that the different positions are alternate.
28:58So how will you remember it?
29:00You remember a cross.
29:024 and 5, cross position.
29:053 and 6, cross position.
29:07But inside, between the two parallel lines only.
29:12Because these are alternate interior angles.
29:16We are talking about the interior.
29:18We are not talking about 1, 2, 7, 8.
29:20That is exterior.
29:22Remember this cross position.
29:24Angle 3 is equal to angle 6.
29:27Angle 4 is equal to angle 5.
29:29What is the reason?
29:30They are alternate interior angles.
29:35And they are always equal if the lines are parallel.
29:40Alternate interior is done.
29:42Now you come to alternate exterior.
29:45Exactly the same.
29:46Let me put a tick here.
29:47Alternate interior is done.
29:49Now we are at alternate exterior angles.
29:53Alternate exterior.
29:55Alternate exterior angles.
29:59Exterior angles means we are not talking about the interior.
30:03Forget it.
30:04Interior angles we have just done.
30:06Alternate interior.
30:07Now we are talking about alternate exterior.
30:10What are the exterior angles?
30:121, 2, 7, 8.
30:15These are exterior angles.
30:17Again the same rule.
30:19One top, one bottom.
30:22One left, one right.
30:24Like we crossed here.
30:26You will apply the same cross on the exterior.
30:301 and 8.
30:32Look at the cross position.
30:352 and 7.
30:37Again cross position.
30:39Where is 1?
30:401 is up and on the right hand side.
30:431 is down and on the left hand side.
30:46This is upper left hand side.
30:49This is lower right hand side.
30:51Opposite should be opposite.
30:53So here angle 2 is equal to angle 7.
30:57Angle 1 is equal to angle 8.
31:00What is the reason?
31:01They are the pair of alternate exterior angles.
31:05Let me just show you once again.
31:08External angles.
31:10Angle 1.
31:11This angle.
31:12And angle 8.
31:14This angle.
31:14They are of different sizes.
31:16One is up, one is down.
31:18One is on the left, one is on the right.
31:19In the similar manner.
31:21We are not talking about this region.
31:27Exterior 1.
31:28In the similar manner.
31:30This angle 7 and angle 2.
31:327 is down and 2 is up.
31:357 is on the left of the transversal.
31:377 is on the right of the transversal.
31:39Okay.
31:40So whenever two lines are given to you as parallel to each other.
31:45Alternate interior as well as alternate exterior angles are equal to each other.
31:51Understood?
31:53It's just like you need to revisit the video once again.
31:57Practice the questions.
32:00It will become very handy for you.
32:04Now the last pair of angles which is left out.
32:07And again very important.
32:10Co-interior angles.
32:16Co-interior angles.
32:18We have the clue again.
32:20Which angles are we talking about?
32:22Interior angle.
32:24In the interior, 1, 2, 7, 8.
32:28This is not possible.
32:30In the interior, it can't be other than 3, 4, 5, 6.
32:34Co means together.
32:37Co-interior.
32:44Right of what?
32:45Right of transversal or left of transversal.
32:48So co-interior are the angles which lie on the same side of the transversal.
32:55Your transversal is the red one.
32:58We said interior angles which are on the same side of the transversal.
33:054 and 6.
33:08See, 4 is on the right hand side and 6 is on the right hand side of the transversal.
33:143 is on the left and 5 is on the left.
33:17Okay?
33:18Now what is the property?
33:19The sum of co-interior angles.
33:22If the two lines are parallel, they are always supplementary.
33:28If I add these two angles, the sum should always be 180.
33:33In the similar manner, if you add these two angles, 3 and 5,
33:37the sum should always come as 130 degree.
33:41And what is the reason?
33:42They are co-interior.
33:45Should I tell you again?
33:46If I have two parallel lines, one transversal,
33:50these two angles which are on the same side of the transversal.
33:55If I call this 4 and this 6, then 4 plus 6 angles.
34:00This is the name of the angle.
34:01It's not the measure.
34:03Angle 4 plus angle 6 should always be equal to 180, reason being co-interior.
34:09If I call this angle A and this angle B,
34:12see, both are on the left side of the transversal and both are in the interior.
34:17So, A plus B will always be 180 degree when the two lines are parallel to each other.
34:28Let us do one question which includes all these concepts which we have learned so far.
34:40Let me do this question for you.
34:42First of all, it has to be erased so that you understand
34:46what I am asking about.
34:48If I say the value of this angle is 60 degree.
35:01And of course, at each step, you need to mention which property have you used.
35:11Which angle is vertically opposite to 2?
35:152 and 1 are directly connected.
35:172 and 4 are directly connected.
35:20So, which angle is not directly connected to 2?
35:23You see, alternate.
35:25Like this.
35:25Vertically opposite.
35:27So, angle 2 and angle 3 are vertically opposite.
35:31So, you will write angle 2 equal to angle 3.
35:34What is the measure?
35:3560 degree.
35:36And the reason is vertically opposite angle.
35:40The value of angle 3 is 60 degree.
35:43Now, let us apply the second concept.
35:46Angle 1 and angle 2.
35:48Are they making a linear pair?
35:51Absolutely.
35:51They are the angles on the straight line.
35:53What is the sum of the linear pair?
35:56180.
35:57If angle 2 is 60 degree, then what is the sum of angle 1?
36:02Angle 1 plus angle 2.
36:05It is 180 degree.
36:07What is the reason?
36:08They are making a linear pair.
36:10So, angle 1 is 180 minus angle 2.
36:14Angle 2 is 60.
36:15What is the value of angle 1?
36:17120 degree.
36:18The value of angle 1 is 120 degree.
36:21We used a linear pair.
36:23Angles on a straight line.
36:24Now, angle 1 and angle 4.
36:27They are vertically opposite angles.
36:29If angle 1 is 120, then angle 4 is also 120.
36:34It is vertically opposite.
36:36It is up to here.
36:37It is a linear pair.
36:38We used a vertically opposite pair.
36:40These four angles are here.
36:42Now, there is a relationship between the upper and lower angles.
36:47Angle 2 and angle 6.
36:50Are they on the same level?
36:52You can see that 2 and 6 are on the same level.
36:55They are corresponding angles.
36:57What is the value of angle 6?
36:5860 degree.
36:59The reason is corresponding.
37:02In the similar manner.
37:03Angle 4.
37:05Lower angle.
37:06Angle 8.
37:07Lower angle.
37:08This is also corresponding.
37:10Angle 4 and angle 8 are in the same position.
37:13If 4 is 120, then 8 should also be 120.
37:16This is also 120.
37:18In a similar manner.
37:20What is the value of angle 5?
37:22It is in the same position.
37:23You can see.
37:24Angle 5.
37:25Angle 1.
37:26Similar position.
37:27Corresponding.
37:28Angle 5 is also 120 degree.
37:31Angle 3 and angle 7.
37:33Corresponding.
37:34It is again 60 degree.
37:36It is easy, isn't it?
37:37Only one angle was given.
37:39We have used the properties and all the angles are found.
37:43Now I ask you.
37:45If this angle.
37:47I told you that angle 4 is 120 degree.
37:50Can you tell me what is the value of angle 5?
37:554 and 5 are both interior.
37:58One is at the top.
37:59One is at the bottom.
38:00One is on the right.
38:01One is on the left.
38:02What do we call such angles?
38:04Alternate interior angles.
38:06And they are equal.
38:07So if angle 4 is 120.
38:10Then angle 5 should also be 120.
38:12Alternate interior.
38:14Okay.
38:15Angle 3 and angle 5.
38:17Are they on the same side of transversal?
38:20Isn't it?
38:21We call the same side of transversal as co-interior.
38:25Whose sum is always 180.
38:27So the sum of angle 3 and angle 5 should be 180.
38:31So what is the answer for angle 3?
38:33It is 60 degree.
38:34Why?
38:35The sum of these two is 180.
38:36Co-interior.
38:38Now angle 3 and angle 6.
38:41How are they?
38:42These are alternate interior.
38:44Cross position.
38:45Angle 6 is also 60 degree.
38:48In the similar manner.
38:49I can still find out what is the value of angle 1, 2, 7 and 8.
38:54Okay.
38:55So this is all about the different kind of angles.
38:59That we have to learn in the times.
39:01This chapter lines and angles.
39:03What you are supposed to do now.
39:05Please do your exercise questions.
39:07NCRT questions.
39:08Only two exercises are there.
39:10I will try to make one another video.
39:13Wherein I will covering the exercises 5.1 and 5.2.
39:17Till then if you still find difficulty in any of the angles.
39:21And you want me to explain any particular topic.
39:24Do not forget to comment.
39:26Okay.
39:27Please like, subscribe and share this video.
39:31Right.
39:31I will wait for your compliments and comments.
39:34And please, please, please don't forget to subscribe to my channel.
39:38Thank you so much for watching it.
39:40Take care.
39:57Bye.