Question

A company is manufacturing a gear in the shape of a regular polygon. The measure of each angle of the gear is 162º. How many sides does the gear have? 19 18 20 21

Answer 1

Ok so here goes
\(162=(n-2)*\dfrac{180}{n}\\162n=180(n-2)\\162n=180n-360\\-18n=-360\\18n=360\\\=20\)

Answer 2

(n-2)180/n=162,
162n=(n-2)180,
162n=180n-360
18n=360
n=20
Hope this helps