Question

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

Answer 1

∠POY = 90° (Given)

Let ∠a and ∠b = 2x and 3x.

Since XOY is a straight line.

So, ∠a + ∠b + ∠POY = 180°     ...(Linear pair)

⇒ 2x + 3x + 90°= 180°

⇒ 5x = 180° − 90°

⇒ 5x = 90°

⇒ x = ${\displaystyle \frac{90°}{5}}$

⇒ x = 18°

Now, ∠a = 2 × 18°

= 36°

∠b = 3 × 18°

= 54°

Here, MON is also a straight line.

∠b + ∠c = 180°     ...(Linear pair)

∠54° + ∠c = 180°

⇒ ∠c = 180° − 54°

∴ c = 126°

Thus, the required measure of c = 126°.