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.

`∠A = 57^o,∠ E = 73^o`

TO FIND: measure of `∠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

`(AB)/(DE)=(AC)/(DE)` And

`∠ A=∠D`

Then, `ΔABC∼ Δ DEF` 

So,

`∠ A=∠D` 

`∠D= 57^circ`

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

`∠A + ∠B + ∠C = 180^circ`

`57^circ + 73^circ + ∠C= 180^circ`

`130^circ + ∠C =180^circ`

`∠C= 50^circ`