Rachel measures the angles of a certain pentagon $A B C D E$ in degrees. She finds that $\angle A<\angle B<\angle C<\angle D<\angle E$, and also that the angle measures form an arithmetic progression, meaning that $\angle B-\angle A=\angle C-\angle B=\angle D-\angle C=\angle E-\angle D$.

What was the measure of $\angle C$ ?
The answer is 108 degrees. Indeed, in a pentagon the sum of the angles is $180 \cdot 3=540$ degrees. Also, in an arithmetic progression the middle term is the average, which is $\frac{1}{5} \cdot 540=108$.