Enter the total number of sides of a (simple) polygon into the calculator to determine the sum of the interior angles. For regular polygons (all sides/angles equal), this calculator can also evaluate the number of sides when given a single interior angle, the sum of interior angles, or an exterior angle.
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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) * 180^\circ
- Where A is the sum of all interior angles
- n is the total number of sides of the polygon
For a regular polygon (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?
- 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.
- 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
An interior angle is the angle inside a polygon at a vertex, formed by two adjacent sides.
