Let's do this question in the figure Abes parallel to Siri, and it's given angle AP is 50 degree angle
P R, B is 130 degrees.
The question is find QPR.
All right.
We need to find QPR, which is this angle over here.
Now pause the video, give it a try and then let's do it together.
All right, in this question, it's mentioned that ABC is parallel to Katie, right?
So there are multiple ways in which you can solve this question.
For example, we can see that angle.
AP our right angle.
AP our.
And angle B, out B.
And will be Aadi, they should be equal, right, because they are alternating triangles and over here
it's given that this angle is 130 degrees and APRA is equal to a P plus QPR.
Right.
Because this full measure is what is equal to 120 degree.
And this full measure is 50 plus the angle that we need to find out the 50 plus.
Let me call this as X 50 plus X will be equal to 130 and I can find X as 80 degrees.
That is one way of solving it, right?
So X is equal to 80 degrees.
Now, let's try one more method.
So it's always helpful to approach a question in multiple angles to solidify our foundation.
Let's move on over here.
We can see that angle p q are will be equal to àngel a p q right.
Because these two lines are parallel.
Therefore this angle over here and this angle over here are also alternating angles.
Right.
So because you are just this angle over here will be equal to a P Q which is this angle over here.
Therefore we can mark this angle as 50 degree will pick you up and APIC you both are 50 degrees already.
Now applying the concept of linear pair, we can see that angle B, R, Q plus one thirty degree has
to be 180 degrees.
Right, because this angle over here and this angle over here on a linear pair.
Right.
Therefore we can see that angle p r Q is 180 minus 130, which is equal to 50 degrees.
All right, let's model over here now.
Over here.
You can see that angle Q, R, B, which is this angle Q, R, P, that's what we've marked as 50 will
be equal to angle B, B, R, which is this angle over here.
Right.
Why will they be equal.
Because they are also alternating angles.
Right.
In that case P R is acting as the transversal and we know abs parallel to Cerutty.
Therefore this angle over here will be equal to BPR, which is also fifty degrees because of this.
Right.
Let's model over here and we can see that over here we are having a straight angle.
So 50 plus X plus 50 should give us 180 degrees.
Right.
So that's a P Q which is this angle over here, QPR, which is this angle QPR.
Right.
And BPR, which is this angle over here B, B, R.
But when you add them you should get 180 degrees, therefore you have 50 plus 50 plus X is equal 180
in that way.
Also you can find that QPR is equal to 180 degrees.
And later in this class we will learn that the some of the angles in a triangle is equal to 180 degrees.
Therefore in that way also you can find excess at because over here you have two angles which are 50
and 50.
The 50 plus 50 plus X is equal to 180 degrees.
So therefore also X should be 80 degrees.
So we have discussed three ways in which this problem can be approached and the correct answer is option
C, which is eighty degrees.