Angles of a Polygon

Interior Angles of a Polygon

The sum of the interior angles of a polygon is dependent on the number of sides the polygon has. For example, the sum of the interior angles of a triangle is 180°, a quadrilateral is 360°, a pentagon is 540°, and a hexagon is 720°. Use the following equation to determine what the sum of the interior angles of a polygon is:

Sum of Interior Angles = 180°*(n – 2)

Where n is the number of sides the polygon has.

Exterior Angles of a Polygon

While the sum of the interior angles of a polygon is dependent on the number of sides the polygon has, the sum of the exterior angles of a polygon is always 360°, regardless of how many sides the polygon has. It is important to note that the exterior angles of a polygon are linear pairs to the interior angles of a polygon. See the below figure for an example:

Polygon with angles.png

In the above figure ∠1, ∠2, ∠3, ∠4, and ∠5 are interior angles and ∠6, ∠7, ∠8, ∠9, and ∠10 are exterior angles. Using the previously discussed relationships:

Sum of Interior Angles = 180º * (n – 2)

This is a five-sided figure so = 5

Sum of Interior Angles = 180º * (5 – 2)

Sum of Interior Angles = 180º * 3

Sum of Interior Angles = 540º

∠1 +∠2 + ∠3 + ∠4 +∠5 = 540º

Conversley the sum of the exterior angles is:

∠6 + ∠7 + ∠8 + ∠9 + ∠10 = 360º

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