Angles in Any Polygon

However you pushed C, the four angles made 360°. Here is why. A diagonal is a line from one corner to a corner that is not next to it. One diagonal cuts the quadrilateral into two triangles. Each triangle has 180°, and $2\cdot 180^{\circ} = 360^{\circ}$.

This works for any polygon. A polygon is a closed shape with straight sides. Draw every diagonal from one corner. A polygon with n sides and no dent splits into n − 2 triangles. So its angles add up to $\left(n-2\right)\cdot 180$ degrees. A polygon with a dent has the same total.

5 sides, 3 triangles: 3 × 180° = 540°