What Is The Formula For The Number Of Sizes Of A Regular Polygon If The Measurement Of Each Interior Angle Is Given?

what is the formula for the number of sizes of a regular polygon if the measurement of each interior angle is given?

 

Answer:

Formula:

Given measure of an interior angle = (n-2)(180)/n

Where n = number of sides

Step-by-step explanation:

Application of the formula:

Given measure of an interior angle of a polygon: 108°

To find the number of sides (n) of the regular polygon:

108 = (n-2)(180)/n

108n = (n-2)(180)

108n = 180n - 360

180n - 108n = 360

72n = 360

72n/72 = 360/72

n = 5

Therefore, the number of sides of a regular polygon given the measure of each interior angle at 108° is 5.

The regular polygon with 5 sides is pentagon.