Interior and Exterior Angles of Polygons

If we imagine the polygon as a house, the interior angles live inside of the house, while the exterior angles live in exile outside of the house.

We can find the sum of interior angles in a shape with $n$ sides using the formula:$$\text{sum of interior angles}=180^{\circ }\times (n-2)$$Just remember that a triangle has $180^{\circ }$, and we can fit $n-2$ triangles in a shape with $n$ sides.The sum of exterior angles for all simple polygons is always $360^{\circ }$ - see how they form a circle when we combine them?We can use these sums to solve for missing angles inside and outside of polygons.