CPM Homework Help : CCG Problem 12-22

A pentagram is a $5$ ‑pointed star that has congruent angles at each of its outer vertices. Use the fact that all regular pentagrams can be inscribed in a circle to find the measure of angle $a$ at right.

Step 1:

Find the measure of each of the intercepted arcs.

$\frac{360^\circ}{5} = 72^\circ$

Step 2(a):

The degree measure of an inscribed angle is half the measure of the intercepted arc.

$\frac{72^\circ}{2}$

Answer:

$=36^\circ$

5‑pointed star with a pentagon in the interior and isosceles triangles connected to each of the sides. The interior angle of the pentagon is, c. The vertical angle of c, is b. The angle of each of the star points is, a. The angle of the triangle base is, d.