#### Answer

m$\angle$1=36$^{\circ}$
m$\angle$2=108$^{\circ}$

#### Work Step by Step

Let x equal the measure of an arc between two points of the pentagram.
x=$\frac{360}{5}$
x=72$^{\circ}$
m$\angle$1=$\frac{x}{2}$
m$\angle$1=$\frac{72}{2}$
m$\angle$1=36$^{\circ}$
m$\angle$2=.5(2x+x)
m$\angle$2=.5(144+72)
m$\angle$2=108$^{\circ}$