Find the measure of each exterior angle of a regular polygon whose central angle measures 120 degrees.
see previous post for method.
To find the measure of each exterior angle of a regular polygon, we can use the formula:
Exterior angle = 360 degrees / Number of sides
In this case, since the central angle measures 120 degrees, the central angle is equal to the interior angle of the polygon. Since the sum of the interior angles of a polygon is given by the formula:
Sum of interior angles = (Number of sides - 2) * 180 degrees
We can now set up an equation:
120 degrees = (Number of sides - 2) * 180 degrees / Number of sides
To simplify the equation, we can cancel the degrees:
120 = (Number of sides - 2) * 180 / Number of sides
Multiply both sides by the number of sides to eliminate the fraction:
120 * Number of sides = (Number of sides - 2) * 180
Distribute the 180:
120 * Number of sides = 180 * Number of sides - 360
Combine like terms:
120 * Number of sides - 180 * Number of sides = -360
Rearrange the equation:
-60 * Number of sides = -360
Divide both sides by -60:
Number of sides = -360 / -60
Number of sides = 6
Now, we can substitute the value of the number of sides into the formula for the measure of each exterior angle:
Exterior angle = 360 degrees / Number of sides
Exterior angle = 360 degrees / 6
Exterior angle = 60 degrees
Therefore, the measure of each exterior angle of the regular polygon is 60 degrees.
To find the measure of each exterior angle of a regular polygon, you can use the formula:
Measure of each exterior angle (E) = 360 degrees ÷ number of sides (n)
In this case, the central angle of the regular polygon measures 120 degrees.
The relationship between the central angle and the exterior angle of a regular polygon is given by:
Central angle + Exterior angle = 180 degrees
So, we can rearrange this equation to get the measure of each exterior angle:
Exterior angle = 180 degrees - Central angle
Substituting the given value:
Exterior angle = 180 degrees - 120 degrees
Exterior angle = 60 degrees
Therefore, each exterior angle of the regular polygon measures 60 degrees.