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Question

Points A,B,Q,D, and C lie on the circle shown and the measures of arcs BQ and QD are 42^ and 38^ respectively. The sum of the measures of angles P and Q is FIGURE

Accepted Answer

We see that the measure of P equals (BD-AC)/2, and that the measure of Q equals AC/2. Since BD = BQ + QD = 42^ + 38^ = 80^, the sum of the measures of P and Q is BD/2 = 80^/2 = 40^ 40^.