2017 AMC 12A Problem 11

Problem 11 of 25IntermediateAlgebra Geometry

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?

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Solution

If the polygon has

n

sides and the forgotten angle is

\alpha,

then

(n-2)180=2017+\alpha.

Since

0\lt\alpha\lt180,

2017\lt(n-2)180\lt2197.

The only multiple of

180

in this range is

2160=(14-2)180,

n=14

and

\alpha=2160-2017=143.

Thus, the correct answer is D.