$ riangle ABC$ and $ riangle PQR$ are shown in the adjoining figures. The measure of $\angle C$ is :

Question

$	riangle ABC$ and $	riangle PQR$ are shown in the adjoining figures. The measure of $\angle C$ is :

Accepted Answer

## Model Answer **(d) 40°** By SSS similarity, △ABC ~ △RQP (since AB/RQ = BC/QP = CA/PR = 1/2). So ∠C = ∠P. In △PQR, ∠P = 180° − 80° − 60° = **40°**, therefore ∠C = 40°. ## Explanation This is directly from Example 5 of the textbook (Chapter 6, Section 6.4). The key step is identifying the correct correspondence: A↔R, B↔Q, C↔P. Once △ABC ~ △RQP is established by SSS, ∠C corresponds to ∠P, and ∠P is found by the angle sum property. Examiners expect you to state the similarity criterion and the correct symbolic form of similarity.

Mathematics — CBSE Class 10 board question