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Let's do this question in the figure Abes parallel to Siri, and it's given angle AP is 50 degree angle

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P R, B is 130 degrees.

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The question is find QPR.

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All right.

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We need to find QPR, which is this angle over here.

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Now pause the video, give it a try and then let's do it together.

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All right, in this question, it's mentioned that ABC is parallel to Katie, right?

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So there are multiple ways in which you can solve this question.

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For example, we can see that angle.

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AP our right angle.

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AP our.

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And angle B, out B.

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And will be Aadi, they should be equal, right, because they are alternating triangles and over here

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it's given that this angle is 130 degrees and APRA is equal to a P plus QPR.

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Right.

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Because this full measure is what is equal to 120 degree.

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And this full measure is 50 plus the angle that we need to find out the 50 plus.

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Let me call this as X 50 plus X will be equal to 130 and I can find X as 80 degrees.

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That is one way of solving it, right?

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So X is equal to 80 degrees.

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Now, let's try one more method.

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So it's always helpful to approach a question in multiple angles to solidify our foundation.

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Let's move on over here.

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We can see that angle p q are will be equal to àngel a p q right.

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Because these two lines are parallel.

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Therefore this angle over here and this angle over here are also alternating angles.

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Right.

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So because you are just this angle over here will be equal to a P Q which is this angle over here.

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Therefore we can mark this angle as 50 degree will pick you up and APIC you both are 50 degrees already.

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Now applying the concept of linear pair, we can see that angle B, R, Q plus one thirty degree has

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to be 180 degrees.

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Right, because this angle over here and this angle over here on a linear pair.

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Right.

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Therefore we can see that angle p r Q is 180 minus 130, which is equal to 50 degrees.

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All right, let's model over here now.

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Over here.

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You can see that angle Q, R, B, which is this angle Q, R, P, that's what we've marked as 50 will

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be equal to angle B, B, R, which is this angle over here.

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Right.

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Why will they be equal.

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Because they are also alternating angles.

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Right.

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In that case P R is acting as the transversal and we know abs parallel to Cerutty.

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Therefore this angle over here will be equal to BPR, which is also fifty degrees because of this.

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Right.

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Let's model over here and we can see that over here we are having a straight angle.

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So 50 plus X plus 50 should give us 180 degrees.

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Right.

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So that's a P Q which is this angle over here, QPR, which is this angle QPR.

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Right.

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And BPR, which is this angle over here B, B, R.

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But when you add them you should get 180 degrees, therefore you have 50 plus 50 plus X is equal 180

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in that way.

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Also you can find that QPR is equal to 180 degrees.

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And later in this class we will learn that the some of the angles in a triangle is equal to 180 degrees.

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Therefore in that way also you can find excess at because over here you have two angles which are 50

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and 50.

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The 50 plus 50 plus X is equal to 180 degrees.

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So therefore also X should be 80 degrees.

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So we have discussed three ways in which this problem can be approached and the correct answer is option

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C, which is eighty degrees.