Question

An interior angle of a regular polygon is ten less than eighteen times the measure of its exterior angle. How many sides does the polygon have?

Answer 1

The polygon has 36 sides

Explanation:

The formula for the interior angle of a polygon is (n-2)180

Thus, the individual interior angle will be [180(n-2)]/n

The measure of the total exterior angle of a polygon is 360. The measure of each exterior angle will be 360/n

Now, from the question, we know that the interior angle is 10 less than 18 times the exterior angle

Mathematically, that means

18(360/n) - 10 = [(n-2)180]/n

Opening the brackets we have;

6480/n - 10 = [(n-2)180]/n

(6480 - 10n)/n = [(n-2)180]/n

Now since n is common as the denominator on both sides, we can eliminate it.

6480 - 10n = 180n- 360

Collect like terms

6480 + 360 = 180n + 10n

190n = 6840

n = 6840/190

n = 36