Problem:
Claire adds the degree measures of the interior angles of a convex polygon and arrives at a sum of 2017. She then discovers that she forgot to include one angle. What is the degree measure of the forgotten angle?
Answer Choices:
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Solution:
If the polygon has sides and the degree measure of the forgotten angle is , then . Because
which implies that , the angle sum is 2160 , and . To see that such a polygon exists, draw a circle and a central angle of measure , and divide the minor arc spanned by the angle into 12 small arcs. The polygon is then formed by the two radii and 12 small chords, as illustrated.
The problems on this page are the property of the MAA's American Mathematics Competitions