CPM Homework Help : GC Problem 12-47

5‑pointed star with a pentagon in the interior and isosceles triangles connected to each of the sides. The angle of each of the star points is, a. A regular 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:

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

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

Answer:

$= 36°$