anairamitch1804 wrote:

The sum of the interior angle measures for any n-sided polygon equals 180(n – 2). If Polygon A has interior angle measures that correspond to a set of consecutive integers, and if the median angle measure for Polygon A is 140°, what is the smallest angle measure in the polygon?

(A) 130°

(B) 135°

(C) 136°

(D) 138°

(E) 140°

We need to first determine the number of sides (or angles) of polygon A. Let n denote the number of sides of polygon n. Since the interior angle measures correspond to consecutive integers, the median angle measure is also the average angle measure. Since sum = average x quantity, we have sum = 140n. Since we are also given that the sum of the interior angle measures equals 180(n - 2), it must be true that 140n = 180(n - 2). Thus:

140n = 180(n - 2)

140n = 180n - 360

-40n = -360

n = 9

We now know polygon A is a 9-sided polygon and there must be 4 angles that have measures less than the median angle measure (and 4 angles that have measures greater than the median angle measure). Since the median angle measure is 140 degrees and the angle measures are consecutive integers, the smallest angle measure must be 140 - 4 = 136 degrees.

Answer: C

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