Question

The measure of an exterior angle of a regular polygon is given below. Find the measure of an interior angle. Then find the number of sides. 36

Answer 1

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: