Question

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

Answer 1

∠XOP + ∠POY = 180° 

∵ straight supplementary 

∠XOP + 90° =180° 

∴∠XOP = 180° – 90° = 90° 

But, ∠XOP = a + b = 90° 

a : b = 2 : 3 

2 + 3 = 5 

Ratio Ratio 5 means 90°

= \(\frac{2\times90}{5}\) = 2 x 18 = 36°

∴ If a = 36° then, ∠b = 54°. 

∠XOM = ∠YON = b = 54° (∵ Vertically opposite angles) 

∠XON + ∠YON = 180° (∵v Straight angle) 

∴ c + 54° = 180° 

c = 180 – 54 

∴ c = 126°.