An angle is a measure of a turn, for example between the two lines that form the internal corners of a polygon.

Angles are measured in degrees (°) out of 360. A full turn (as in a circle) is 360°. (Note that a circular shape is not a polygon as it is made up of curves rather than straight lines). 

Number of angles in a polygon

The number of angles within a polygon corresponds to the number of sides, or edges, of the polygon. For example:

• 3 sides (triangle) : 3 angles
• 4 sides (quadrilateral) : 4 angles

Sum of degrees in a polygon

The internal angles of a polygon always add up to the same number of degrees, corresponding to its number of edges.

• 3 angles (triangle): 180°
• 4 angles (quadrilateral): 360°

The sum of degrees in the angles of a regular polygon can be confirmed using the following formula:

180° × (n - 2)

where n is the polygon's number of edges.

For example a pentagon has 5 sides, so n - 2 is 5 - 2 = 3. The internal angles, therefore, add up to 180° × 3 = 540°.

Try it out

What is the sum of angles in a hexagon (6 sided polygon)?

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