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smc

geometry senior

Problem

Claire adds the degree measures of the interior angles of a convex polygon and arrives at a sum of . She then discovers that she forgot to include one angle. What is the degree measure of the forgotten angle?
(A)
(B)
(C)
(D)
Solution
We know that the sum of the interior angles of the polygon is a multiple of . Note that and , so the angle Claire forgot is . Since the polygon is convex, the angle is , so the answer is .
Final answer
D