Answer:
The measure of angle C is [tex]90\°[/tex]
Step-by-step 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
[tex]m<A=35\°[/tex]
[tex]m<E=55\°[/tex] -------> [tex]m<B=m<E[/tex] ------> [tex]m<B=55\°[/tex]
Find the measure of angle C
[tex]m<A+m<B+m<C=180\°[/tex]
substitute and solve for m<C
[tex]35\°+55\°+m<C=180\°[/tex]
[tex]m<C=90\°[/tex]
