Find the measures of an interior angle and an exterior angle of a regular polygon with 6 sides.
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To find the measures of an interior angle and an exterior angle of a regular polygon with 6 sides, we can use the following formulas:
1. Interior angle: The formula to find the measure of an interior angle of a regular polygon is given by (n-2) * 180 / n, where n is the number of sides of the polygon.
For a regular polygon with 6 sides, plug in the value of n into the formula:
Interior angle = (6 - 2) * 180 / 6
Simplifying this equation:
Interior angle = 4 * 180 / 6
Interior angle = 720 / 6
Interior angle = 120 degrees
Therefore, the measure of an interior angle of a regular hexagon (a six-sided polygon) is 120 degrees.
2. Exterior angle: The formula to find the measure of an exterior angle of a regular polygon is given by 360 / n, where n is the number of sides of the polygon.
For a regular polygon with 6 sides, plug in the value of n into the formula:
Exterior angle = 360 / 6
Exterior angle = 60 degrees
Therefore, the measure of an exterior angle of a regular hexagon is 60 degrees.