Interior and exterior angles
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Summary
Interior and exterior angles
In a nutshell
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 and are internal angles. The angle 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 .
Finding the interior angles of a regular polygon
The sum of the interior angles of a polygon can be found using the formula:
Where is the sum of the interior angles, and 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 by the number of sides.
Example 2
What is the size of an interior angle of a regular nonagon?
A nonagon has sides, so . The sum of the interior angles is therefore given to be:
To find the size of one interior angle, divide this number by :
The size of one interior angle of a nonagon is .
Finding the exterior angles of a regular polygon
Exterior angles of a regular polygon always add up to . Therefore, the formula for one exterior angle is given to be:
Where is the size of one exterior angle, and is the number of sides.
Example 3
What is the size of one exterior angle of a regular nonagon?
Substitute into the formula to give:
The size of one exterior angle of a regular nonagon is .
Note: Notice how the interior and exterior angle of a regular nonagon adds up to .
FAQs - Frequently Asked Questions
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.