A polygon is a closed shape with many sides.

E.g. triangle, square, rhombus, decagon

In this tutorial, you are going to see how the interior angles and exterior angles vary in polygons, depending on the number of sides. You can choose the number of sides of a polygon and see how the interior and exterior angles change.

The Sum of Interior Angles

The sum of interior angles of a polygon, T, is given by,
T = (n-2)(180, where n is the number of sides.

Based on the following image, you can see that there is a connection between the number of triangles in a polygon and the sum of interior angles of the polygon.

Polygon Sum
PolygonNo of SidesNo of Triangles InsideSum of Interior Angles
Triangle311 x 180
Square422 x 180
Pentagon533 x 180
Hexagon644 x 180
Heptagon755 x 180
Octagon866 x 180
Nonagon977 x 180
Decagon1088 x 180

If the sides of a polygon are equal, it is called a regular polygon. In a regular polygon, the interior angles are equal.

The Sum of Exterior Angles

The angle between a side and the the extended adjacent side is called exterior angle.

Polygon exterior angle

The sum of exterior angles add up to 3600. For a regular polygon of sides n,
Exterior angle = 360 / number of sides

Polygon Maker - interactive practice

With the following applet, you can practise interior and exterior angles of a polygon.



Recommended Reading


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