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

Given that,

The lines and intersect at O.

From the figure, XOY is a straight line and its angle is 180°

So, ∠XOM + ∠MOP + ∠POY = 180°

From the given, Let ∠a = 2x and ∠b = 3x

⇒∠b + ∠a + ∠POY = 180°----(1)

Given that ∠POY = 90°

Substitute the values in equation (1),

⇒2x + 3x + 90° = 180°

⇒5x + 90° = 180°

⇒5x = 180°-90° = 90°

⇒x =

∴ x = 18°

⇒ ∠a = 2x = 2×18° = 36°

⇒ ∠b = 3x = 3×18° = 54°

From the figure, MON is a straight line and its angle is 180°

⇒∠b + ∠c = 180°

⇒54° + ∠c = 180°

⇒∠c = 180°-54°

∴ ∠c = 126°