Question
11.
A company is manufacturing a gear in the shape of a regular polygon. The measure of each angle of the gear is 162ยบ. How many sides does the gear have?
20
21
19
18
A company is manufacturing a gear in the shape of a regular polygon. The measure of each angle of the gear is 162ยบ. How many sides does the gear have?
20
21
19
18
Answers
GPT 3.5
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
\( (n-2) \times 180 = 162n \)
Solving for n:
\( 180n - 360 = 162n \)
\( 18n = 360 \)
\( n = 20 \)
Therefore, the gear has 20 sides.
So the answer is: 20