Interior and exterior angles refer to specific angles in a shape (or polygon). There are formulae that can be used to calculate the interior and exterior angles of regular polygons.

Definitions

A polygon is another word to describe a 2D shape.

A regular polygon is a 2D shape that has equal sides and angles.

An interior angle of a polygon is the inner angle formed by two sides of a shape.

An exterior angle of a polygon is the formed by extending one side of the shape past the vertex.

Example 1

In the diagram above, the angles $\alpha$ and $75\degree$ are internal angles. The angle $135^\circ$ is an external angle.

Note: It is worth noticing that an interior and exterior angle are two angles on a straight line, which means that they add together to make $180\degree$.

Finding the interior angles of a regular polygon

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

$\theta=(n-2)\times180$

Where $\theta$ is the sum of the interior angles, and $n$ is the number of sides.

The interior angles of a regular polygon are equal. Therefore, to find the size of one interior angle, divide the value of $\theta$ by the number of sides.

Example 2

What is the size of an interior angle of a regular nonagon?

A nonagon has $9$ sides, so $n=9$. The sum of the interior angles is therefore given to be:

What is the formula for an exterior angle of a regular polygon?

The exterior angle of a regular polygon is found by calculating 360/n, where n is the number of sides.

What is the formula for the sum of interior angles?

The sum of interior angles of a polygon is (n-2)x180, where n is the number of sides.

What are interior and exterior angles?

An interior angle of a polygon is the inner angle formed by two sides of the shape.
An exterior angle of a polygon is the angle formed by extending one of the lines past the vertex.

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