If $A B C$ and $D E F$ are similar triangles such that $\angle A=47^{\circ}$ and $\angle E=83^{\circ}$, then $\angle C=$
(a) $50^{\circ}$
(b) $60^{\circ}$
(c) $70^{\circ}$
(d) $80^{\circ}$
Given: If ΔABC and ΔDEF are similar triangles such that
$\angle \mathrm{A}=47^{\circ}$
$\angle \mathrm{E}=83^{\circ}$
To find: Measure of angle C
In similar ΔABC and ΔDEF,
$\angle \mathrm{A}=\angle \mathrm{D}=47^{\circ}$
$\angle B=\angle E=83^{\circ}$
$\angle \mathrm{C}=\angle \mathrm{F}$
We know that sum of all the angles of a triangle is equal to $180^{\circ}$.
$\angle \mathrm{A}+\angle \mathrm{B}+\angle \mathrm{C}=180^{\circ}$
$47^{\circ}+83^{\circ}+\angle C=180^{\circ}$
$\angle \mathrm{C}+130^{\circ}=180^{\circ}$
$\angle \mathrm{C}=180^{\circ}-130^{\circ}$
$\angle \mathrm{C}=50^{\circ}$
Hence the correct answer is (a)