The measure of an exterior angle of a regular polugon is given. Find the measure of an interior angle. Then find the number of sides.
1) The measure of the exterior angle is x.
interior is 180-x
# sides is 360/x
To find the measure of an interior angle of a regular polygon, we can use the formula:
Interior angle = 180° - Exterior angle
In this case, the measure of the exterior angle is given as x. Therefore, the measure of the interior angle would be:
Interior angle = 180° - x
To find the number of sides in a regular polygon, we can use the formula:
Number of sides = 360° / Interior angle
In this case, we need to substitute the value of the interior angle (180° - x) into the formula to find the number of sides:
Number of sides = 360° / (180° - x)
Now, you can plug in the value of x, the measure of the exterior angle, to find the measures of the interior angle and the number of sides.