Question

PQRS is a rectangle. Find the angles marked x and y.

Answer 1

Given, PQRS is a rectangle.

In a rectangle, opposite sides are parallel.

Angles opposite to equal sides are equal in a triangle.

∠PQO = 24°

In a rectangle, diagonals are equal and they bisect each other.

Let PR and QS meet at O.

So, we have, OR = OQ

⇒ ∠ORQ = 24°

All interior angles of a rectangle are right angles.

⇒ y + ∠OQR = 90°   ...(∵ ∠RQP = 90°)

⇒ y = 90° – 24° = 66°

We know that the sum of the interior angle of a triangle = 180°

⇒ 24° + x + 24° = 180°

⇒ x = 180° – 48° = 132°

Hence, this is required.