Question

If ABC and DEF are similar triangles such that ∠A = 57° and ∠E = 73°, what is the measure of ∠C?

Answer 1

GIVEN: There are two similar triangles ΔABC and ΔDEF.

${\displaystyle \angle A={57}^o,\angle E={73}^o}$

TO FIND: measure of ${\displaystyle \angle C}$

SAS Similarity Criterion: If in two triangles, one pair of corresponding sides are proportional and the included angles are equal then two triangles are similar.

In ΔABC and ΔDEF if

${\displaystyle \frac{AB}{DE}=\frac{AC}{DE}}$And

${\displaystyle \angle A=\angle D}$

Then, ${\displaystyle \Delta ABC\sim \Delta DEF}$ 

So,

${\displaystyle \angle A=\angle D}$ 

${\displaystyle \angle D={57}^o}$

Now we know that sum of all angles of a triangle is equal to 180°,

${\displaystyle \angle A+\angle B+\angle C={180}^o}$

${\displaystyle {57}^o+{73}^o+\angle C={180}^o}$

${\displaystyle {130}^{\oplus }\angle C={180}^o}$

${\displaystyle \angle C={50}^o}$