Question

In the following figure, lines PQ and ST intersect at O. If ∠POR = 90° and x : y = 3 : 2, then z is equal to ______.

Options

• 126°

• 144°

• 136°

• 154°

Answer 1

In the following figure, lines PQ and ST intersect at O. If ∠POR = 90° and x : y = 3 : 2, then z is equal to 144°.

Explanation:

Since, ∠POR, ∠ROT and ∠TOQ lie on a straight line POQ, then their sum is equal to 180°.

∴ ∠POR + ∠ROT + ∠TOQ = 180°

⇒ 90° + x + y = 180°

⇒ x + y = 180° – 90°

⇒ x + y = 90°  ...(i)

Also, x : y = 3 : 2  ...[Given]

Let x = 3a and y = 2a

∴ 3a + 2a = 90°  ...[From equation (i)]

⇒ 5a = 90°

⇒ a = `90^circ/5` = 18°

Now, x = 3a = 3 × 18° = 54° and y = 2a = 2 × 18° = 36°

Since, y and z form a linear pair.

∴ y + z = 180°

⇒ 36° + z = 180°

⇒ z = 180° – 36°  ...[∵ y = 36°]

⇒ z = 144°