## Exterior angles

The word
exterior means "outside", so an exterior angle is on the outside of a polygon. However, it's not the angle all the way round - in the picture above, you can see that the base line of the triangle has been extended. The exterior angle is the one between this base line and the other edge of the triangle.The interior and exterior angle at any corner or vertex add up to 180°. This is because angles on a straight line equal 180°. If you know the interior angle at one corner, you can work out the size of the exterior angle by subtracting the interior angle from 180°. Imagine walking around the perimeter of a shape. By the time you get back to where you started, you will have completed a full turn (you may want to try doing this with a simple shape like a triangle or a square). A full turn is 360°, so the total exterior angle sum of any polygon is 360°. Regular polygons have equal side lengths and equal angles. A (equilateral) triangle has three equal sides and three equal angles. The total sum of its exterior angles is 360°, so we can share out this total between the three exterior angles (360° ÷ 3). Each exterior angle must be 120°. |

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