What is the measure of each interior angle of an 18 sided polygon?

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Answer:

The measure of each interior angle of an #18#-sided polygon is #160^@#.

Explanation:

First, start with the interior sum formula,

#(n - 2)*180^@#

The variable #n# stands for how many sides of the polygon. This is an #18#-sided polygon, so plug in the sides.

#(18 - 2)*180^@ = 2880^@#

After you find the sum of the interior angles, just divide the sum by how many sides you have.

#2880^@/18 = 160^@#

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Answer:

#160°#

Explanation:

An alternative method is to use the exterior angle.

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the sum of the exterior angles is ALWAYS #360°#

So you can find the size of the exterior angles of a regular polygon quite easily:

If there are #18# sides #(n=18)#, then each exterior angle is:

#(360°)/n = (360°)/18 = 20°#

The sum of the exterior and interior angles is #180°# because they are adjacent angles on a straight line.

#:.# each interior angle is #180° - 20° = 160°#

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