CPM Homework Help : INT2 Problem 10-35

A shaded regular pentagon. An isosceles triangle is attached on each side of the pentagon to create a star. The sides of the triangle that are not attached to the pentagon each have one tick mark. Each angle, opposite the side of the pentagon, labeled question mark. After doing well on a test, Althea’s teacher places a gold star on her paper. When Althea examines the star closely, she realizes that it is really a regular pentagon surrounded by five isosceles triangles, as shown in the diagram at right. What is the measure of each vertex angle of the star? Show all work.

Hint:

What is the measure of each interior angle of a regular pentagon if its total angle sum is $540°$ ?

Help:

Once you have the measures of the pentagon, how can you use these
measures to find the measures of the angles in the isosceles triangles?

More Help:

Use the Triangle Angle Sum Theorem to find the vertex angle of each star point.