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If each exterior angle of a regular polygon measures 40 degrees, the polygon is a nonagon (9-sided polygon).
As the number of sides in a regular polygon increases, the angle increases. This occurs as a function where each interior angle measures (180*(n-2)) / n, where n is the number of sides.
If one interior angle measures 172° then the corresponding exterior angle measures 180 - 172 = 8°. The number of sides = 360 ÷ 8 = 45.
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A regular polygon
The sum of a regular polygon's interior angles is always equal to (n-2) * 180, where n is the number of sides in the polygon. Given that one exterior angle measures 40 degrees, we can find the interior angle by subtracting 40 from 180 degrees (since the exterior and interior angles are supplementary) to get 140 degrees. So, the sum of the interior angles of the regular polygon is 140 * n.
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The interior angle of any regular polygon can be calculated using the formula 180 * (n - 2) / n, where n is the number of sides. In this case, since each exterior angle measures 72 degrees, the interior angle would be 180 - 72 = 108 degrees. So the measures of the interior angles in this regular polygon would be 108 degrees.
Since the interior angle measure of the regular polygon is 140⁰, its exterior angle measure is 180⁰ - 140⁰ = 40⁰. Since the sum of the exterior angle measures is 360⁰, the polygon has 360⁰/40⁰ = 9 sides.
1440 degrees
1440 degrees
divide the number of sides by 171
If each exterior angle of a regular polygon measures 40 degrees, the polygon is a nonagon (9-sided polygon).
5 sides and it is a regular pentagon
1800 degrees
The sum of the exterior angles of a regular polygon = 360° If an exterior angle measures 8° then the number of sides = 360/8 = 45