Calculating Interior Angles of Regular and Irregular Polygons | Formulas and Examples

Interior angle of a polygon

The interior angle of a polygon is the angle formed inside the polygon at each of its vertices

The interior angle of a polygon is the angle formed inside the polygon at each of its vertices. It is the angle between two adjacent sides within the polygon.

To calculate the measure of each interior angle of a regular polygon, you can use the following formula:

Interior angle = (n-2) × 180° / n,

where n represents the number of sides of the regular polygon.

For example, let’s say we have a regular pentagon. Since a pentagon has 5 sides, we can substitute n = 5 in the formula:

Interior angle of a pentagon = (5-2) × 180° / 5
= 3 × 180° / 5
= 540° / 5
= 108°

So, each interior angle of a regular pentagon measures 108 degrees.

If you have an irregular polygon, where the sides and angles may vary, you would need additional information about the specific polygon to calculate the interior angles accurately.

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