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
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