11.

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?

20

21

19

18

1 answer

Since the sum of the interior angles of a polygon can be found using the formula \( (n-2) \times 180 \) where n is the number of sides, we can set up the equation:

\( (n-2) \times 180 = 162n \)

Solving for n:

\( 180n - 360 = 162n \)

\( 18n = 360 \)

\( n = 20 \)

Therefore, the gear has 20 sides.

So the answer is: 20