If ABC and DEF are similar triangles such that ∠A = 47° and ∠E = 83°, then ∠C =
Question:

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) $80^{\circ}$

Solution:

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)