# In Fig. 6.14, lines XY and MN intersect at O. If ∠POY = 90° and a : b = 2 : 3, find c.

**Solution:**

Given: ∠POY= 90° and a : b = 2 : 3.

If two lines intersect with each other, then the vertically opposite angles formed are equal.

Line OP is perpendicular to line XY. Hence ∠POY = ∠POX = 90°

∠POX = ∠POM + ∠MOX

90° = a + b ….(1)

Since a and b are in the ratio 2 : 3 that is,

a = 2x and b = 3x ….(2)

Substituting (2) in (1),

a + b = 90°

2x + 3x = 90°

5x = 90°

x = 90°/5 = 18°

a = 2x = 2 × 18°

a = 36°

b = 3x = 3 × 18°

b = 54°

Also , ∠MOY= ∠MOP + ∠POY

= a + 90°

= 36° + 90° = 126°

Lines MN and XY intersect at point O and the vertically opposite angles formed are equal.

∠XON = ∠MOY

c = 126°

**☛ Check: **NCERT Solutions for Class 9 Maths Chapter 6

**Video Solution:**

## In Fig. 6.14, lines XY and MN intersect at O. If ∠POY = 90° and a : b = 2 : 3, find c.

NCERT Solutions Class 9 Maths Chapter 6 Exercise 6.1 Question 2

**Summary:**

If the given figure lines XY and MN intersect at O, given that ∠POY = 90°, and a : b = 2 : 3, thus, ∠XON = c = 126°.

**☛ Related Questions:**

- In Fig. 6.13, lines AB and CD intersect at O. If ∠AOC + ∠BOE = 70° and ∠BOD = 40°, find ∠BOE and reflex ∠COE.
- In Fig. 6.15, ∠PQR = ∠PRQ then prove that ∠PQS = ∠PRT.
- In Fig. 6.16, if x + y = w + z, then prove that AOB is a line.
- In Fig. 6.17, POQ is a line. Ray OR, is perpendicular to line PQ. OS another ray lying between rays OP and OR. Prove that ∠ROS = 1/2 (∠QOS - ∠POS).

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