Answer: The measure of an exterior angle of a regular polygon is given by the formula:
(n-2) * 180 / n
Where n is the number of sides of the polygon.
So, if the measure of an exterior angle of a polygon is 36 degrees, we can set up the equation:
(n-2) * 180 / n = 36
To find the measure of an interior angle, we can use the formula:
(n-2) * 180 / n = (n-2) * 180 / n
So, if the measure of an exterior angle is 36, the measure of an interior angle would be:
(n-2) * 180 / n = (n-2) * 180 / n = (n-2) * 180 / n = (n-2) * 180 / n = (n-2) * 180 / n = (n-2) * 180 / n = (n-2) * 180 / n
To find the number of sides, we can use the formula:
n = (180 / (180-x))
So, if the measure of an exterior angle is 36, the number of sides would be:
n = (180 / (180-36)) = (180 / 144) = 5
Therefore, a regular polygon with an exterior angle measure of 36 degrees has 5 sides and an interior angle measure of 144 degrees.
Explanation: