+817 Points $A$, $B$, $Q$, $D$, and $C$ lie on the circle shown and the measures of arcs $BQ$ and $QD$ are $30^\circ$ and $30^\circ$, respectively. Find the sum of the measures of angles $P$ and $Q$, in degrees.
+129771 minor arc BD = 30° + 30° = 60°
We have this relationship
Angle P = (1/2) ( minor arc BD - minor arc AC)
2 Angle P = ( 60 - minor arc AC)
And minor arc AC = 2 * angle Q
So
2*Angle P = 60 - 2* Angle Q
So
2 * Angle P + 2* Angle Q = 60
2 ( Angle P + Angle Q) = 60 divide through by 2
Angle P + Angle Q = 30°
