how many sides does a regular polygon have if the interior angle is 165°
give step-by-step
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The interior and the exterior angles make a linear pair : add up to make 180° .
180° - 165° = 15° measure of one ext. angle.
The sum of the exterior angles of any convex polygon is 360° .
360° ÷ 15° = 24 exterior angles.
Therefore, there are 24 sides of this regular polygon.
Answered by
1
Answer: 24 sides
Step-by-step explanation:
Interior angle of any polygon = 180(n-2) / n
165 = 180 (n-2) / n
165n = 180n - 360
165n - 180n = -360
-15n = -360
n = 24
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