What is the measure of one angle of a regular polygon with 18 sides?

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The sum of the angles of a polygon is given by the formula:

(n-2)(180)

where n is the number of sides, which in this case is 18.

So we will replace n with 18 and evaluate.

(18-2)(180) = (16)(180) = 2880

But this is all the angles, and we just...

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The sum of the angles of a polygon is given by the formula:

(n-2)(180)

where n is the number of sides, which in this case is 18.

So we will replace n with 18 and evaluate.

(18-2)(180) = (16)(180) = 2880

But this is all the angles, and we just want to know one angle.

So we must divide by the number of angles, 18.

2880/18 = 160 degrees

The answer is 160 degrees.

Approved by eNotes Editorial Team
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According to the Interior Angles Sum Theorem, the sum of the measures of the interior angles of a regular polygon with n sides is (n - 2) * 180.  In this example, n = 18 because the polygon has 18 sides.  Substitute 18 in for n to find the sum of the interior angles.

(n - 2) * 180

(18 - 2) * 180

16 * 180

2880

Now we know that the sum of the interior angles is 2880 degrees.  A polygon with 18 sides has 18 interior angles.  Therefore, to find the measure of one of these angles, divide the sum by 18.

2880 / 18 = 160

Answer:  Each angle is 160 degrees.

 

Approved by eNotes Editorial Team