# In Fig. 6.15, ∠PQR = ∠PRQ, then prove that ∠PQS = ∠PRT.

**Solution:**

Given: ∠PQR = ∠PRQ

To prove: ∠PQS = ∠PRT

We know that, if a ray stands on a line, then the sum of adjacent angles formed is 180°.

Let ∠PQR = ∠PRQ = a.

Let ∠PQS = b and ∠PRT = c.

Lines ST and PQ intersect at point Q, hence the sum of adjacent angles ∠PQS and ∠PQR is 180°.

∠PQS + ∠PQR = 180°

b + a = 180°

b = 180° - a….(1)

Lines ST and PR intersect at point R, hence the sum of adjacent angles ∠PRQ and ∠PRT is 180°.

∠PRQ + ∠PRT = 180°

a + c = 180°

c = 180° - a ….(2)

From equations (1) and (2), it is clear that b = c. Hence ∠PQS = ∠PRT is proved.

**Video Solution:**

## In Fig. 6.15, ∠PQR = ∠PRQ then prove that ∠PQS = ∠PRT.

### NCERT Solutions Class 9 Maths - Chapter 6 Exercise 6.1 Question 3:

**Summary:**

In Fig. 6.15, given that ∠PQR = ∠PRQ, hence we have proved that ∠PQS = ∠PRT.