Question

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

Options

• 90°

• 120°

• 150°

• 180°

Answer 1

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

Explanation: 

Step 1: Use the Similarity Property

Since ΔABC ~ ΔPQR, their corresponding angles are equal

∠A = ∠P, ∠B = ∠Q, ∠C = ∠R

From the given information:

∠A = 30∘, ∠Q = 90∘

Since ∠Q corresponds to ∠B, we conclude

∠B = 90∘

Step 2: Find ∠R

In ΔPQR, the sum of all angles is 180°

= ∠P + ∠Q + ∠R = 180∘

= 30∘ + 90∘ + ∠R = 180∘

= ∠R = 180∘ − 120∘ = 60∘

Step 3: Find (∠R + ∠B)

∠R + ∠B = 60∘ + 90∘ = 150∘