Question

Each exterior angle of a regular polygon is 20° . How many sides are there in the

polygon? What is the measure of each interior angle of the regular polygon?

$please \: give \: full \: explanation$
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Answer 1

•ANSWER•

•Sides

SidesSince the sum of the exterior angles of a polygon is 360° and an angle of the regular polygon is 20°, then 360° / 20° is the number of sides. Let the number of sides be n.

•n = 18, an octadecagon.

•Measure of Each Interior Angle

Measure of Each Interior Angle If you imagine a regular octadecagon (or any polygon), you will notice that the exterior angle is the supplement of the interior angle.

•20° = 180° - 1, where 1 is the interior angle.

°[20°] + 1 = [180° -1] + 1

°[20° + 1] - 20° = [180°] - 20°

°1 = 160°

Answer 2

•ANSWER•

•Sides

SidesSince the sum of the exterior angles of a polygon is 360° and an angle of the regular polygon is 20°, then 360° / 20° is the number of sides. Let the number of sides be n.

•n = 18, an octadecagon.

•Measure of Each Interior Angle

Measure of Each Interior Angle If you imagine a regular octadecagon (or any polygon), you will notice that the exterior angle is the supplement of the interior angle.

•20° = 180° - 1, where 1 is the interior angle.

°[20°] + 1 = [180° -1] + 1

°[20° + 1] - 20° = [180°] - 20°

°1 = 160°

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