Question

Given the measure of an interior angle of a regular polygon, how many sides does the polygon have?

Answer 1

The sides of a regular polygon with a known interior angles can be found as follows:

Interior Angle = (n−2) × 180° / n

Regular polygon

A regular polygon is a polygon that have equal sides and equal angles.

A regular polygon has the following angles:

• interior angles
• exterior angles

According to the question, the interior angles are given. To know the number of sides of polygon can be calculated as follows:

Note the interior and the exterior angles add up to 180 degrees.

Therefore,

Interior Angle = 180° − Exterior Angle

Exterior angle = 360°/n

Interior Angle = 180° − 360°/n

n = number of sides

Finally,

• Interior angle = (n−2) × 180° / n

learn more on polygon here:brainly.com/question/7153502?referrer=searchResults