AOB is a straight line. Rays OP and OQ lie on the same side of AB with $\angle AOP = 40^\circ$ and $\angle BOQ = 70^\circ$. Ray OR bisects $\angle POQ$. What is $\angle AOR$?

Explanation

1. 01

   The three angles $\angle AOP$, $\angle POQ$, $\angle QOB$ make the straight angle: $\angle POQ = 180^\circ - 40^\circ - 70^\circ = 70^\circ$.

2. 02

   OR bisects it, so $\angle POR = 35^\circ$.

3. 03

   $\angle AOR = \angle AOP + \angle POR = 40^\circ + 35^\circ = 75^\circ$.