Question

In the given figure, lines PQ, MN, and RS intersect at O. If x : y = 1 : 2 and z = 90°, find ∠ROM and ∠POR.

Answer 1

In the figure, lines PQ, MN and Rs are intersecting each other at O

x : y = 1 : 2, z = 90°

∠MOQ = ∠PON = z .......(Vertically opposite angles)

Now, RS is a straight line

∴ x + z + y = 180°

⇒ x + y + 90° = 180° .........(∵ z = 90°)

⇒ x + y = 180°− 90° = 90°

But x : y = 1 : 2

Let x = a then y = 2a

∴ a + 2a = 90°

⇒ 3a = 90°

⇒ a =`(90°)/3` = 30°

∴ x = 30° and y = 2a = 2 × 30° = 60°

Now, ∠ROM = y = 60°

and ∠POR = ∠SOQ ..........(Vertically opposite angles)

= x = 30°