## Elementary Geometry for College Students (6th Edition)

$m\angle 6=30^{\circ}$
In part e we determined that the $m\angle 2=120^{\circ}$. All radii of a circle are congruent, therefore $\overline{CQ}=\overline{BQ}$, creating an isosceles triangle. The two base angles of an isosceles triangle are congruent. So if we subtract the vertex angle ($\angle 2$) from $180^{\circ}$ and then divide the resulting number by two (two base angles), we will find the measure of the missing angle. $180-120=60\div2=30$ $m\angle 6=30^{\circ}$