Answer:
The measure of angle C is [tex]81\°[/tex]
Step-by-step explanation:
we know that
If AB || DC
then
[tex]m<A+m<D=180\°[/tex] -----> supplementary angles by consecutive interior angles
and remember that the sum of the interior angles in a trapezoid is equal to 360 degrees
[tex]m<A+m<B+m<C+m<D=360\°[/tex]
step 1
Find the measure of angle D
[tex]m<A+m<D=180\°[/tex]
substitute the measure of angle A
[tex]125\°+m<D=180\°[/tex]
[tex]m<D=180\°-125\°=55\°[/tex]
step 2
Find the measure of angle C
[tex]m<A+m<B+m<C+m<D=360\°[/tex]
substitute the values
[tex]125\°+99\°+m<C+55\°=360\°[/tex]
[tex]m<C=360\°-279\°=81\°[/tex]
