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In this video, let's discuss various types of related angles.

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We start with complementary angles.

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When do we see that?

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Two angles are complementary, two angles are complementary.

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If the sum of those two angles is equal to 90 degrees, let's take an example.

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Over here, you have an angle of 30 degree measure and you have another angle of 60 degree measure.

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Now, 30 plus 60 is equal to 90 degrees.

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Therefore, these two angles are complementary and we say that each angle is the complement of the other

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angle.

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All right, let's move on.

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What do we mean with supplementary angles?

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Two angles are set to be supplementary.

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If the sum of the two angles is equal to 180 degrees.

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Let's take an example over here.

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You have an angle of 30 degree measure and this angle over here is 150 degrees measure.

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Now, 30 plus 150 degrees is equal to 180 degrees.

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Therefore, these two angles are supplementary.

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Now, we say that each angle is the supplement of the other.

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Now, it's very important that we do not confuse between these two angles.

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All right.

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Now, some students mistake supplementary angles as complementary and vice versa.

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So to remember that, just have a funny story in your mind.

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Think of somebody who takes some supplements when they go to the gym and then they fall down flat on

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their face.

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So if somebody falls down, they'd be lying like this on the floor.

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Right.

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So in that way, you can remember 180 degrees.

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So supplementary angles are angles which add up to 180 degrees.

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All right.

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We move ahead.

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The next type of related angles which we discuss is a decent angle.

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Let's take an example over here.

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We have two angles.

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This is angle one, and this is angle, too.

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Now, these two angles are different angles.

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Let's try to understand the conditions to call two angles, as are different angles using this example

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so that it'll help us to visualize the same angle.

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One and angle two are adjusted angles.

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What can we observe?

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We can see that these two angles have a common vertex, right?

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This is the common vertex over here already.

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And these two angles have a common arm, right?

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Which is the common arm.

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Let me name these rays.

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Let this be a B, let this be easy and let this rub it.

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In this case, you can see that rib is the common arm red.

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All right, and we can see that the non common items are on either side of the common right, which

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are the non common arms they are AC and ADA and AC is on this side of the common arm, which is AB and

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80 is on this side of the common right.

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So these are the three conditions which determine two angles to be adjusted angles.

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All right, let's move on.

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Let's take one more example over here, you have a few angles formed right now, let's also angle pick

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you as an angle because you are so angle P.

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Q s.

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That's this angle over here and angle P Q ah that's p q ah, that's this angle over here.

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Now you can see that these two angles are not just an angle, right.

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They are not edges and angles.

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Why is that.

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So these are the three criteria for a just an angle.

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Right.

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So do these two angles have a common vertex.

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Yes, they do have a common vertex.

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Right.

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This is the common vertex.

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Guanabara common to these two angles.

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Have a common.

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Yes, BQ is the common arm.

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Right.

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Picou is a common arm for both the angles, but the third criteria is not satisfied.

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You can see that both the known common arms, which is Q, R and Q s are on the same side of P.

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Q Therefore these two angles are not adjacent.

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And you can also note that when you have to adjust and angles, there will be no common interior point

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because of these three criteria's results that in the case of two, are decent angles.

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There will be no common interior point.

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But over here you can see that this point or this point or this point, these points are common interior

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points to both the angles.

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All right, let's move on.

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The next type of angles we discuss is linear bears.

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All right.

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What is a linear pair?

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A linear pair is a pair of decent angles whose known common sites are opposite race.

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Let's take an example over here.

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You can see that the non common arms, that is, let's name it, or eight and Olby in this case or A

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and or B are opposite race.

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Right.

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Therefore, well, here we have a linear pair angle, one and angle to form a linear pair.

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In this case, the non common race.

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Let's take us all at us and all beat us.

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These are not opposite race, right?

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Therefore, this in this case, angle one, an angle two are not a linear pair.

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And you can see that just because of this criteria that the non common sides are opposite race.

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Therefore, whenever you have a linear pair, the sum of the angles will be equal to 180 degrees.

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Or we can see that angle one and angle two are supplementary.

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All right, let's move on.

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The next type of angles which rediscuss is vertically opposite angles.

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All right, now let's do a construction.

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We have two lines.

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Let this be Lynelle and let this be nineham.

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We can see that for angles are formed because they are intersecting now.

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Angled one and angled three are just opposite to each other.

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Right.

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These type of angles are what we call vertically opposite angles.

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Similarly, angle to an angle, four are also vertically opposite angles.

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Now vertically opposite angles will always be equal.

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That is angle one is equal to angle three and angle two is equal to angle for.

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Let's try to quickly prove that to ourselves.

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All right, so what we're here, we're trying to show why vertically opposite angles are equal now you

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can see that angle one and angle two are forming a linear pair, right?

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Because the non-government sides are opposite race.

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Therefore, angle one plus angle two is equal to 180 degrees.

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Right.

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Similarly, you can see that angle to angle three.

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Also form a linear pair.

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Right.

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Therefore, angle to plus angle three is also equal to 180 degrees.

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Now, because these two are equal, I can see angle one plus angle two is equal to angle two plus angle

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three.

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Right now we have angle to an angle to in both the sides on the left hand side and the right hand side

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of the equation.

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So let's cancel that out.

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And we are left with angle one is equal to angle three.

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Right.

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Similarly, we can also prove that angle two is equal to angle four.

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Therefore, in the case of vertically opposite angles, they will be equal.

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All right.

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Let's quickly revise what we have learned.

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We have learned that complementary angles add up to 90 degree.

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We have learned that supplementary angles add up to 180 degrees.

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We have seen the three criteria to determine whether two angles are adjusted angles.

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We have learned what we mean with the linear pair.

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And if you have a linear pair, if you add the angles, you will get 180 degree or a linear pair is

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supplementary.

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And we have seen what we mean with vertically opposite angles and vertically opposite angles are equal

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to each other.