If ΔBPQ ≅ ΔASR and ∠A = 1/3 ∠R = ∠S, then find ∠Q. (All angles are in degrees).

If ΔBPQ ≅ ΔASR and ∠A = 1/3 ∠R = ∠S, then find ∠Q. (All…

If ΔBPQ ≅ ΔASR and ∠A = $\frac{1}{3}$ ∠R = ∠S, then find ∠Q. (All angles are in degrees).

Show answer & explanation

Correct answer: A

Explanation

The correct answer is Option 1 i.e. 108°.

Given:

ΔBPQ ≅ ΔASR

∠ A = 1/3 ∠ R = ∠ S

Concept Used:

The sum of all angles of a triangle is 180°.

Suppose two triangles ABC and PQR are congruent, then

∠A = ∠P, ∠B = ∠ Q, ∠C = ∠R

Explanation:

Let the value of ∠A is x.

So, ∠R = 3x and ∠S = x.

So, in triangle ASR, ∠A + ∠S + ∠R = 180°

⇒ x + x + 3x = 180

⇒ 5x = 180

⇒ x = 36°

Since ΔBPQ ≅ ΔASR, ∠Q = ∠R

∠Q = 3x = 3 × 36 = 108

Hence the value of ∠Q is 108°.