### Home > CCG > Chapter 12 > Lesson 12.1.2 > Problem12-22

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.

Find the measure of each of the intercepted arcs.

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

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

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

$=36^\circ$