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If each interior angle of a regular polygon has a calculated as of 144 degrees, Determine the numbers of sides does it have?
a. 8
b. 9
c. 10
d. 11
c. The measure of an angle of a regular polygon of n sides is n - 2 × 180. Since each angle calculates 144°, we will answer for n, the number of sides. Using the formula 144 = n - 2 × 180, answer for n. Multiply both sides by n, 144n = (n - 2)180. Divided by 180, 144n = 180n - 360. Subtract 180n from both sides, -36n = -360. Divide both sides by -36, n = 10. The polygon has 10 sides.
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