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 two figures are similar, then the ratio of its corresponding sides is equal and its corresponding angles are congruent

In this problem

m<A=m<D

m<B=m<E

m<C=m<F

we have that

`m<A=35\°`

`m<E=55\°`

so

m<B=m<E

`m<B=55\°`

Remember that

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

`m<A+m<B+m<C=180\°`

substitute values and solve for m<C

`35\°+55\°+m<C=180\°`

`m<C=180\°-90\°=90\°`