Answer:
The measure of angle C is [tex]90\°[/tex]
Step-by-step 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
[tex]m<A=35\°[/tex]
[tex]m<E=55\°[/tex]
so
m<B=m<E
[tex]m<B=55\°[/tex]
Remember that
The sum of the interior angles in a triangle must be equal to 180 degrees
[tex]m<A+m<B+m<C=180\°[/tex]
substitute values and solve for m<C
[tex]35\°+55\°+m<C=180\°[/tex]
[tex]m<C=180\°-90\°=90\°[/tex]
