Answer
$m\angle 5=50^{\circ}$
Work Step by Step
In part d we determined that the $m\angle 1=80^{\circ}$. All radii of a circle are congruent, therefore $\overline{BQ}=\overline{AQ}$, creating an isosceles triangle. The two base angles of an isosceles triangle are congruent. So if we subtract the vertex angle ($\angle 1$) from $180^{\circ}$ and then divide the resulting number by two (two base angles), we will find the measure of the missing angle.
$180-80=100\div2=50$
$m\angle 5=50^{\circ}$
