Calculate each interior angle of a regular polygon from its number of sides, plus the angle sum and exterior angle, or find the sides from an angle.

Each angle assumes a regular polygon (equal sides and angles). The angle sum applies to any simple polygon.

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Interior Angle Formula

The following formula can be used to calculate the sum of the interior angles of any simple polygon (in degrees).

A = (n - 2) ร— 180^ยฐ
  • Where A is the sum of all interior angles
  • n is the total number of sides of the polygon

For a regular convex polygon (all sides and all interior angles equal), you can calculate a single interior angle by dividing the sum of the interior angles by the number of sides. (In radians, the sum is A = (n - 2)ฯ€.)

Interior Angle Definition

An interior angle is the angle formed inside a polygon at a vertex by two adjacent sides.

Interior Angle Example

How to calculate the sum of interior angles?

  1. First, determine the number of sides.

    Count the total number of sides of the polygon you are looking at. For example, a square would have 4 sides and a pentagon would have 5 sides.

  2. Next, calculate the sum.

    Determine the total sum of the interior angles using the formula A = (n-2)*180 (degrees). For example, for a pentagon this would equal (5-2)*180 = 3*180 = 540 degrees.

FAQ

What is an interior angle?

An interior angle is the angle inside a polygon at a vertex, formed by two adjacent sides.