Find the measure of each interior angle of a regular polygon whose central angle measures 60 degrees.
well, the central angle is the same as the exterior angle...
Or, you have an isosceles triangle with vertex of 60. The interior angles are made up of two of the triangles' base angles.
To find the measure of each interior angle of a regular polygon, we can use the following formula:
Interior Angle = 180° - Central Angle
Given that the central angle measures 60 degrees, we can substitute this value into the formula:
Interior Angle = 180° - 60°
Simplifying, we have:
Interior Angle = 120°
Therefore, each interior angle of the regular polygon measures 120 degrees.
To find the measure of each interior angle of a regular polygon, we can use the formula:
Interior Angle = (180 * (n - 2)) / n
where n is the number of sides in the polygon.
Since you are given that the central angle measures 60 degrees, we can use the relationship between the central angle and the interior angle:
Central Angle = 360 degrees / n
Solving for n in terms of the central angle, we have:
n = 360 degrees / Central Angle
Substituting the given value of the central angle as 60 degrees, we get:
n = 360 degrees / 60 degrees
n = 6
So, the regular polygon has 6 sides. Now, we can substitute this value into the formula for the interior angle:
Interior Angle = (180 * (n - 2)) / n
Interior Angle = (180 * (6 - 2)) / 6
Interior Angle = (180 * 4) / 6
Interior Angle = 120 degrees
Therefore, each interior angle of the regular polygon with a central angle of 60 degrees measures 120 degrees.