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.
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.
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.