We already know that the sum of angles in a triangle is $180$180°.

What about the sum of angles in a quadrilateral? Well a quadrilateral can be thought of as two triangles, so the internal angle sum is $180+180=360$180+180=360°

This interactive will show you different interior angle sums for different polygons. You can also see how many triangles fit into it.

Watch this video if you would like to see this interactive in action -

If $n$n represents the number of sides, then the number of triangles in any polygon is $n-2$n−2.

If each triangle has $180$180°, then the total interior angle sum of a polygon is $180\times\left(n-2\right)$180×(n−2)

Sum of Exterior Angles of a Polygon

Why is the sum of the exterior angles of any convex polygon always 360°?

Why is the result the same for a 3-sided polygon (i.e. a triangle) as for a 20-sided polygon?

To see why, imagine you are driving a car around this polygonal track. What is the total of the angles you turn when doing 1 complete lap. These angles are the external (exterior) angles of the polygon. What is the sum?

Make sure you keep the polygon convex (no concave structures). See here to remind yourself the difference between convex and concave.

Watch this video if you would like to see this interactive in action -