Question

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

Answer 1

In the figure, lines XY and MN 

intersect at O and ∠ POY = 90°.

Also, given a : b = 2 : 3 

Let a = 2x and b = 3x. 

Since, ∠XOM + ∠POM + ∠POY = 180° 

(Linear pair axiom) 

⇒ 3x + 2x + 90° = 180° 

⇒ 5x = 180° – 90° 

⇒ x = 90 5 ° = 18° 

∴ ∠XOM = b = 3x = 3 × 18° = 54° 

and ∠POM = a = 2x = 2 × 18° = 36° 

Now, ∠XON = c = ∠MOY = ∠POM + ∠POY 

(Vertically opposite angles) 

= 36° + 90° = 126° 

Hence, c = 126° Ans.