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?
A. 21
B. 18
C. 20
D. 19

Answer 1

the rule for the individual angle measurement of a (regular) n-sided polygon is \((n-2) × \dfrac{180}{n}
\)

Answer 2

we're solving for n here, so we have \(162=(n-2)*\dfrac{180}{n}\\162n=180(n-2)\\162n=180n-360\\-18n=-360\\18n=360\\n=20\)

Answer 3

Thanks (: @bibby

Answer 4

np ;)