Given that ∆ABC ~ ∆DEF and the corresponding sides AB, BC, and CA of ∆ABC match with DE, EF, and DF of ∆DEF respectively; If ∠A = 47° and ∠E = 83°, then what is the measure of ∠C?

Q.Given that ∆ABC ~ ∆DEF and the corresponding sides AB, BC, and CA of ∆ABC match with DE, EF, and DF of ∆DEF respectively; If ∠A = 47° and ∠E = 83°, then what is the measure of ∠C?

\(\because\) ∆ABC ~ ∆DEF \(\therefore\) ∠B = ∠E = 83° \(\therefore\) ∠C = 180° − (∠A + ∠B) = 180° − (47° + 83°) = 180° − 130° = 50° ∴ ∠C = 50°