Question

△ABC is similar to △DEF by the ​ AA Similarity Postulate ​ .

What is the measure of ∠C?



Enter your answer in the box.

Answer 1

AA Similarity Postulate means Angle Angle Congruency which means that <A and <D are both 55° and <B and <E are both 60°

So, to solve for C, since a triangle has a total of 180° you subtract 180-55-60 to get C.

m<C = 65°

Hope this helped :)

Answer 2

`m<C=65\°`

Explanation:

we know that

If two triangles are similar, then its corresponding angles are congruent

so

m<A=m<D

m<C=m<F

m<B=m<E

step 1

Find the measure angle B

we have

`m<E=60\°`

so

`m<B=60\°` ------> by corresponding angles

step 2

Find the measure angle C

we know that

`m<A+m<B+m<C=180\°` ----> the sum of the interior angles in a triangle must be equal to
`180\°`

we have

`m<A=55\°`

`m<B=60\°`

substitute

`55\°+60\°+m<C=180\°`

`m<C=180\°-55\°-60\°=65\°`