Interior and exterior angle sums of a polygon

How to use it

1. 1With the sum known, one unknown angle follows from a single linear equation in the others.
2. 2Going the other way, a known interior-angle sum gives $n$ from $n=\frac{S}{180^{\circ }}+2$.
3. 3When the angles are all equal, the exterior-angle route $\frac{360^{\circ }}{n}$ is usually the faster one.
4. 4For a hexagon the sum is $720^{\circ }$, for a pentagon $540^{\circ }$, for a quadrilateral $360^{\circ }$.

Step-by-step

1. 1
   $S=\left(5-2\right)\times 180^{\circ }=540^{\circ }$

   Why: A pentagon splits into three triangles.

2. 2
   $100+110+120+130=460$
3. 3
   $540^{\circ }-460^{\circ }=80^{\circ }$