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^o`

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

`∠A + ∠B+∠ C= 180^o `

`57^o +73^o +∠C= 180^o`

`130^o+∠C =180^o`

`∠C= 50^o`