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All interior angles of a regular polygon are equal. The formula that gives the measure of the interior angle of a regular polygon is:
(n-2)*180/n, where n is the number of sides.
In this case, the regular polygon has 18 sides:
(n-2)*180/n = (18-2)*180/18
(18-2)*180/18 = 16*10 = 160 degrees
The measure of one angle of the regular polygon whose number of sides is 18, is of 160 degrees.
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
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.
The sum of the angles of a polygon is given by the formula:
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.
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