Each interior angle of a regular polygon measures 160^. How many sides does the polygon have?

Each interior angle of a regular polygon measures 160^. How... | SAT Lines, angles, and triangles Question, Answer Explained

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Math · Geometry and TrigonometryMedium

Each interior angle of a regular polygon measures $160^\circ$ . How many sides does the polygon have?

$9$

$16$

$18$

$20$

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Answer: C

Each exterior angle measures $180^\circ - 160^\circ = 20^\circ$ . The exterior angles of any polygon sum to $360^\circ$ , so the polygon has $\frac{360}{20} = 18$ sides.

Choice D is the measure, in degrees, of each exterior angle, not the number of sides.

Why the other choices are wrong

A. This divides 180 by 20, but the exterior angles sum to 360 degrees.
B. 16 is the number of sides minus 2, the value of n minus 2 in the angle sum formula.
D. 20 degrees is the measure of each exterior angle, not the number of sides.

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