Question

"Question 5 In the given figure, if AB || CD, ∠APQ = 50º and ∠PRD = 127º, find x and y.

Class 9 - Math - Lines and Angles Page 104"

Answer 1

x=50degrees y= 77degrees

Answer 2

Alternate angles:

When two lines are crossed by another line the pair of angles on opposite sides of the transversal is called alternate angles.

 

Theorem 1

If a transversal intersects two Parallel Lines then each pair of alternate interior angles is equal.

Theorem 2

If a transversal intersects two lines such that a pair alternate interior angle is equal then the two lines are parallel.

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Solution:

 

Here, AB||CD & transversal PQ intersects them at P &  Q.

∠PQR=∠APQ

[Alternate interior angles]

 

X=50°   [∠APQ=50°(given)]

∠PQR=50°

 

AB||CD & transversal PR intersects them at P &  R.

∠APR=∠PRD (alternate interior angles)

(∠APQ+∠QPR)=127°

[∠PRD=127°(given)]

 

50°+y= 127°

Y= 127- 50=77°

 

Hence, x= 50° & y= 77°

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Hope this will help you