Given $\triangle ABC \sim \triangle PQR$, $\angle A = 30°$ and $\angle Q = 90°$. The value of $(\angle R + \angle B)$ is
Generated by claude-sonnet-4-6 · 2026-06-15 10:26 · grounding rag
Model Answer
Option (C) 150°
Since △ABC ~ △PQR, corresponding angles are equal: ∠A = ∠P = 30°, ∠B = ∠Q = 90°, ∠C = ∠R.
In △PQR: ∠P + ∠Q + ∠R = 180° → 30° + 90° + ∠R = 180° → ∠R = 60°.
Therefore, ∠R + ∠B = 60° + 90° = 150°.
Source: Criteria for Similarity of Triangles, Chapter 6
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Explanation
- In similar triangles, corresponding angles are equal in the order of naming: A↔P, B↔Q, C↔R.
- ∠Q = 90° means ∠B = 90° (corresponding angles).
- Use the angle sum property in △PQR to find ∠R = 60°.
- A common mistake is to assume ∠R = ∠Q = 90°; always check correspondence carefully.