Question

\(△ABC∼△PQR\) if \(∠A = 50°\), then \(∠Q+ ∠R =\)

• A. 130°
• B. 40°
• C. 80°
• D. 140°

Answer 1

The Correct Option is A

Correct answer: 130° 

Explanation:
Given: \( \triangle ABC \sim \triangle PQR \) and \( \angle A = 50^\circ \) In similar triangles, corresponding angles are equal. So: \[ \angle A = \angle P = 50^\circ \] The sum of all angles in a triangle is: \[ \angle P + \angle Q + \angle R = 180^\circ \] Substituting \( \angle P = 50^\circ \): \[ 50^\circ + \angle Q + \angle R = 180^\circ \Rightarrow \angle Q + \angle R = 180^\circ - 50^\circ = 130^\circ \]

Hence, \( \angle Q + \angle R = {130^\circ} \)