How to Calculate the Measure of Interior Angles in a Polygon: Formulas and Examples

Interior Angles

Interior angles are angles that are formed inside a polygon

Interior angles are angles that are formed inside a polygon. They are created by connecting two sides of the polygon with a line. Each interior angle is formed by three consecutive vertices (corners) of the polygon.

To find the measure of an interior angle in a polygon, you can use the following formula:

Interior Angle = (n-2) x 180 / n

In this formula, “n” represents the number of sides of the polygon. By substituting the value of “n” into the formula, you can calculate the measure of each interior angle.

For example, let’s say we have a regular hexagon (a polygon with six sides). By substituting “n = 6” into the formula, we get:

Interior Angle = (6-2) x 180 / 6
Interior Angle = 4 x 180 / 6
Interior Angle = 720 / 6
Interior Angle = 120 degrees

So, each interior angle in a regular hexagon measures 120 degrees.

In general, the sum of all interior angles in a polygon is given by the formula:

Sum of Interior Angles = (n-2) x 180

Using this formula, you can find the total measure of all interior angles in any polygon by substituting the value of “n”.

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