Finding the Sum of the Interior Angles of a Polygon
(KS2, Year 6)
The sum of the interior angles of a polygon is found using the formula:

polygons sum of interior angles 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?
interior angles of a pentagon example

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°.

Lesson Slides

The slider below shows another real example of how to find the sum of the interior angles of a polygon.

What Are the Interior Angles of a Polygon?

The interior angles of a polygon are the angles between two sides, inside the shape.

Why Does the Formula Work?

Any polygon can be split into a number of triangles, each of which has interior angles adding up to 180°.sum_interior_angles_polygons_explainedThe number of triangles is 2 less than the number of sides and there are there are 180° of interior angles for every triangle:
(n − 2) × 180°
This is why the formula works.
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This page was written by Stephen Clarke.