How to find the measure of an interior angle of a regular polygon?

A polygon is a two-dimensional geometric figure that has a finite number of sides. The sides of a polygon are made of straight line segments connected to each other end to end. They can have any number of sides. Regular polygons have sides and angles of the same length. Many of the polygons like triangles, squares, and rectangles are used extensively for various purposes.

Answer: To find the measure of an interior angle of a regular polygon, we make use of the formula for each angle = (n - 2) × 180 / n. 

The formula calculated is only valid in cases of regular-sided polygons.

Explanation: 

We use the standard formula (n - 2) × 180 to find the sum of the interior angles of an n-sided polygon. 

To find the measure of one interior angle, we divide the result by n.

For example, let's consider a 3-sided regular polygon, that is, an equilateral triangle. We use the formula, and substitute n with 3.

We get the result to be 180. 

Now, if we divide it by n, that is, 3, we get 60, which is the measure of an interior angle of a triangle.

Note: The particular formula is true for only regular polygons, that is, where all the angles are the same, and does NOT cover other cases.

Hence, to find the measure of an interior angle of a regular polygon, we use the formula angle = (n - 2) × 180 / n.