If $\Delta ABC \sim \Delta DEF$ such that $\angle A = 47^\circ$ and $\angle E = 83^\circ$, then $\angle C$ is equal to:
(a) $50^\circ$
(b) $60^\circ$
(c) $70^\circ$
(d) $80^\circ$
Step-by-Step Solution
Key Concept: Corresponding angles of similar triangles are equal. In $\Delta ABC$: $\angle A = 47^\circ, \angle B = \angle E = 83^\circ$.
$\angle B = \angle E = 83^\circ$. In $\Delta ABC$: $\angle A + \angle B + \angle C = 180^\circ$. [0.5 Mark]
$47^\circ + 83^\circ + \angle C = 180^\circ \Rightarrow 130^\circ + \angle C = 180^\circ \Rightarrow \angle C = 50^\circ$. [0.5 Mark]
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🎯 Official CBSE Marking Scheme:
Setting $\angle B = \angle E = 83^\circ$: 0.5 Mark
Calculating $\angle C = 50^\circ$: 0.5 Mark
Correct Answer: $50^\circ$