Question

Find the number of sides of a convex polygon if the measures of its interior angles have a sum of 21,240°.

Answer 1

$18(n - 2) = 1240 \degree \\ 18n - 36 = 1240 \\ 18n = 1240 - 36 \\ 18n = 1204 \\ n = 67$

Subtract the interior angle from 180. For example, if the interior angle was 165, subtracting it from 180 would yield 15. Divide 360 by the difference of the angle and 180 degrees. For the example, 360 divided by 15 equals 24, which is the number of sides of the polygon.

Answer 2

18(n−2)=1240°

18n−36=1240

18n=1240−36

18n=1204

n=67

Subtract the interior angle from 180. For example, if the interior angle was 165, subtracting it from 180 would yield 15. Divide 360 by the difference of the angle and 180 degrees. For the example, 360 divided by 15 equals 24, which is the number of sides of the polygon.