Question

Given ΔABC ~ ΔPQR, ∠A = 30° and ∠Q = 90°. The value of (∠R + ∠B) is ______.

Options

• 90°

• 120°

• 150°

• 180°

Answer 1

Given ΔABC ~ ΔPQR, ∠A = 30° and ∠Q = 90°. The value of (∠R + ∠B) is 150°.

Explanation: 

Given, ΔABC ~ ΔPQR and ∠A, ∠P = 30°, ∠Q = 90°

∠A = ∠P = 30°

∠B = ∠Q = 90°

In any triangle, the sum of the interior angles is 180°.

∠R = 180° – (∠P + ∠Q)

∠R = 180° – (30° + 90°)

∠R = 180° – 120°

∠R = 60°

∠R + ∠B

= 60° + 90°

= 150°