# In Fig. 6.32, if AB || CD, ∠APQ = 50° and ∠PRD = 127°, find x and y

**Solution:**

Given: AB || CD, ∠APQ = 50° and ∠PRD = 127°

To Find: x and y

When a ray intersects a line, the sum of adjacent angles formed is 180°.

When two parallel lines are cut by a transversal, alternate interior angles formed are equal.

AB and CD are parallel lines cut by transversal PQ hence the alternate interior angles formed are equal.

∠APQ = ∠PQR and hence x = 50°.

Similarly, AB and CD are parallel lines cut by transversal PR hence the alternate angles formed are equal.

∠APR = ∠PRD = 127°

∠APQ + ∠QPR = ∠PRD = 127°

50° + y = 127°

y = 127° - 50°

y = 77°

**Video Solution:**

## In Fig. 6.32, if AB || CD, ∠APQ = 50° and ∠PRD = 127°, find x and y

### NCERT Maths Solutions Class 9 - Chapter 6 Exercise 6.2 Question 5:

**Summary:**

In Fig. 6.32, if AB || CD, ∠APQ = 50°, and ∠PRD = 127°, then the values of x and y are 50° and 77° respectively.