Question

∆ABC ~ ∆DEF. If ∠A=35° and ∠E=55°, what is the measure of ∠C?

Answer 1

The measure of angle C is
`90\°`

Explanation:

we know that

If the triangle ABC is similar to triangle DEF

then

the corresponding angles are congruent

so

In this problem

m<A=m<D

m<B=m<E

m<C=m<F

Remember that the sum of the interior angles in a triangle must be equal to 180 degrees

we have

`m<A=35\°`

`m<E=55\°` ------->
`m<B=m<E` ------>
`m<B=55\°`

Find the measure of angle C

`m<A+m<B+m<C=180\°`

substitute and solve for m<C

`35\°+55\°+m<C=180\°`

`m<C=90\°`