Exterior Angles of a Polygon
(KS2, Year 6)
The LessonThe exterior angles of a polygon are the angles outside of the polygon, between a side and the extension of the side next to it.
The Sum of the Exterior Angles of a PolygonThe sum of the exterior angles of a polygon is:
The exterior angles of a polygon add up to 360°, a full revolution.
The Exterior Angles of a Regular PolygonRegular polygons have equal exterior angles. There are as many exterior angles as there are sides. To find each exterior angle in a regular polygon, divide the sum of the exterior angles by the number of sides. The formula for each of the exterior angles of a regular polygon is:
ExampleImagine you wanted to find an interior angle of a regular hexagon.
A regular hexagon has 6 sides, so n = 6. Using the formula:
Exterior angle = 360° ÷ n Exterior angle = 360° ÷ 6 Exterior angle = 60°Each angle in a regular hexagon is 60°. Read more about how to find the exterior angle of a regular polygon
The Exterior Angles of Different Polygons
|Shape||Sum of Exterior Angles||Exterior Angle of Regular Polygon|
What Exterior Angles Are...The exterior angle is the angle between a side and the extension of the side next to it.
...And What Exterior Angles Are NotThe exterior angle of a polygon is not the angle outside of a polygon, between two sides.
What Is a Polygon?A polygon is a 2-dimensional shape with straight sides.
Interior AnglesPolygons have interior angles as well as exterior angles.
The sum of the interior angles of a polygon is given by the formula:
An Interior and Exterior Angle in a Polygon Add Up to 180°An interior and exterior angle in a polygon add up to 180°.
Read more about how the interior and exterior angle of a polygon add up to 180°
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