In this video, let's discuss various types of related angles.
We start with complementary angles.
When do we see that?
Two angles are complementary, two angles are complementary.
If the sum of those two angles is equal to 90 degrees, let's take an example.
Over here, you have an angle of 30 degree measure and you have another angle of 60 degree measure.
Now, 30 plus 60 is equal to 90 degrees.
Therefore, these two angles are complementary and we say that each angle is the complement of the other
angle.
All right, let's move on.
What do we mean with supplementary angles?
Two angles are set to be supplementary.
If the sum of the two angles is equal to 180 degrees.
Let's take an example over here.
You have an angle of 30 degree measure and this angle over here is 150 degrees measure.
Now, 30 plus 150 degrees is equal to 180 degrees.
Therefore, these two angles are supplementary.
Now, we say that each angle is the supplement of the other.
Now, it's very important that we do not confuse between these two angles.
All right.
Now, some students mistake supplementary angles as complementary and vice versa.
So to remember that, just have a funny story in your mind.
Think of somebody who takes some supplements when they go to the gym and then they fall down flat on
their face.
So if somebody falls down, they'd be lying like this on the floor.
Right.
So in that way, you can remember 180 degrees.
So supplementary angles are angles which add up to 180 degrees.
All right.
We move ahead.
The next type of related angles which we discuss is a decent angle.
Let's take an example over here.
We have two angles.
This is angle one, and this is angle, too.
Now, these two angles are different angles.
Let's try to understand the conditions to call two angles, as are different angles using this example
so that it'll help us to visualize the same angle.
One and angle two are adjusted angles.
What can we observe?
We can see that these two angles have a common vertex, right?
This is the common vertex over here already.
And these two angles have a common arm, right?
Which is the common arm.
Let me name these rays.
Let this be a B, let this be easy and let this rub it.
In this case, you can see that rib is the common arm red.
All right, and we can see that the non common items are on either side of the common right, which
are the non common arms they are AC and ADA and AC is on this side of the common arm, which is AB and
80 is on this side of the common right.
So these are the three conditions which determine two angles to be adjusted angles.
All right, let's move on.
Let's take one more example over here, you have a few angles formed right now, let's also angle pick
you as an angle because you are so angle P.
Q s.
That's this angle over here and angle P Q ah that's p q ah, that's this angle over here.
Now you can see that these two angles are not just an angle, right.
They are not edges and angles.
Why is that.
So these are the three criteria for a just an angle.
Right.
So do these two angles have a common vertex.
Yes, they do have a common vertex.
Right.
This is the common vertex.
Guanabara common to these two angles.
Have a common.
Yes, BQ is the common arm.
Right.
Picou is a common arm for both the angles, but the third criteria is not satisfied.
You can see that both the known common arms, which is Q, R and Q s are on the same side of P.
Q Therefore these two angles are not adjacent.
And you can also note that when you have to adjust and angles, there will be no common interior point
because of these three criteria's results that in the case of two, are decent angles.
There will be no common interior point.
But over here you can see that this point or this point or this point, these points are common interior
points to both the angles.
All right, let's move on.
The next type of angles we discuss is linear bears.
All right.
What is a linear pair?
A linear pair is a pair of decent angles whose known common sites are opposite race.
Let's take an example over here.
You can see that the non common arms, that is, let's name it, or eight and Olby in this case or A
and or B are opposite race.
Right.
Therefore, well, here we have a linear pair angle, one and angle to form a linear pair.
In this case, the non common race.
Let's take us all at us and all beat us.
These are not opposite race, right?
Therefore, this in this case, angle one, an angle two are not a linear pair.
And you can see that just because of this criteria that the non common sides are opposite race.
Therefore, whenever you have a linear pair, the sum of the angles will be equal to 180 degrees.
Or we can see that angle one and angle two are supplementary.
All right, let's move on.
The next type of angles which rediscuss is vertically opposite angles.
All right, now let's do a construction.
We have two lines.
Let this be Lynelle and let this be nineham.
We can see that for angles are formed because they are intersecting now.
Angled one and angled three are just opposite to each other.
Right.
These type of angles are what we call vertically opposite angles.
Similarly, angle to an angle, four are also vertically opposite angles.
Now vertically opposite angles will always be equal.
That is angle one is equal to angle three and angle two is equal to angle for.
Let's try to quickly prove that to ourselves.
All right, so what we're here, we're trying to show why vertically opposite angles are equal now you
can see that angle one and angle two are forming a linear pair, right?
Because the non-government sides are opposite race.
Therefore, angle one plus angle two is equal to 180 degrees.
Right.
Similarly, you can see that angle to angle three.
Also form a linear pair.
Right.
Therefore, angle to plus angle three is also equal to 180 degrees.
Now, because these two are equal, I can see angle one plus angle two is equal to angle two plus angle
three.
Right now we have angle to an angle to in both the sides on the left hand side and the right hand side
of the equation.
So let's cancel that out.
And we are left with angle one is equal to angle three.
Right.
Similarly, we can also prove that angle two is equal to angle four.
Therefore, in the case of vertically opposite angles, they will be equal.
All right.
Let's quickly revise what we have learned.
We have learned that complementary angles add up to 90 degree.
We have learned that supplementary angles add up to 180 degrees.
We have seen the three criteria to determine whether two angles are adjusted angles.
We have learned what we mean with the linear pair.
And if you have a linear pair, if you add the angles, you will get 180 degree or a linear pair is
supplementary.
And we have seen what we mean with vertically opposite angles and vertically opposite angles are equal
to each other.