外角定理

The exterior angle theorem states that the measure of an exterior angle of a triangle is greater than either of the measures of the remote interior angles.

Proof. First, look at this diagram. Note, here, that $\angle 4$ is the exterior angle. Now, note that from the Triangle Angle Sum theorem, $\angle 1 + \angle 2 + \angle 3 = 180^\circ$ and $\angle 3 + \angle 4= 180^\circ$ since they are supplementary. Hence: $$\angle 3 = 180^\circ - \angle 1 - \angle 2 = 180^\circ - \angle 4 \implies \angle 4 = \angle 1 + \angle 2,$$and this is what we wanted to show. $\Box$

I'm attaching the same worksheet as I did for a different explanation. However, I only wish for you to do questions 11-20, and also, rather than doing the calculation $180º - \theta$, please use the exterior angle theorem and divide $360º$ by the amount of sides in the polygon.