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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.

 

 Aug 17, 2023
 #1
avatar+128398 
+1

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°

 

 

cool cool cool

 Aug 17, 2023

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