How to Find the Sum of the Interior Angles of a Polygon

Finding the Sum of the Interior Angles of a Polygon

The sum of the interior angles of a polygon is found using the formula:

In this formula, n is the number of sides of the polygon.

The formula tells you what the interior angles of a polygon add up to.

How to Find the Sum of the Interior Angles of a Polygon

Finding the sum of the interior angle of a polygon is easy.

Question

What is the sum of the interior angles of a pentagon?

Step-by-Step:

1

Start with the formula:

Sum of interior angles = (n − 2) × 180°

2

Substitute the number of sides into the formula.

A pentagon has 5 sides. In our example, n = 5.

Sum of interior angles = (5 − 2) × 180°

Sum of interior angles = 3 × 180°

Sum of interior angles = 540°

Answer:

The sum of the interior angles of a pentagon is 540°.

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See Also

What is an angle?