2017 AMC 12A Problem 11

Attempt Problem 11 of the 2017 AMC 12A below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2017 AMC 12A solutions, or check the answer key.

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11.

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?

37

63

117

143

163

The true angle sum

(n-2)\cdot180

is a multiple of

180

just above

2017

The forgotten angle is that multiple minus

2017,

and it must be less than

180

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.

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