Question

Given: ABCD is a trapezoid with AB || DC. If m∠A = 125 and m∠B = 99, find m∠C/

Answer 1

The measure of angle C is
`81\°`

Explanation:

we know that

If AB || DC

then

`m<A+m<D=180\°` -----> supplementary angles by consecutive interior angles

and remember that the sum of the interior angles in a trapezoid is equal to 360 degrees

`m<A+m<B+m<C+m<D=360\°`

step 1

Find the measure of angle D

`m<A+m<D=180\°`

substitute the measure of angle A

`125\°+m<D=180\°`

`m<D=180\°-125\°=55\°`

step 2

Find the measure of angle C

`m<A+m<B+m<C+m<D=360\°`

substitute the values

`125\°+99\°+m<C+55\°=360\°`

`m<C=360\°-279\°=81\°`