# If the measure of each interior angle of a regular polygon is 171, what is the number of sides in the polygon?

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The polygon will have 40 sides.

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The measure of the interior angles of a polygon is determined by the formula

were

We know that the interior angles of the polygon in the question have measures of

The polygon will have 40 sides.

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Use the exterior angle to find there are

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The interior angle and the exterior angle of a polygon are adjacent supplementary angles. This means that they add to

Each exterior angle

The sum of the exterior angles of any polygon is

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