The sum of the angles in a triangle is $180^\circ,$ so we have $\angle P + \angle Q + \angle R = 180^\circ$.
We are given that $\angle P + \angle Q = 60^\circ,$ so we can substitute this into the equation to get $60^\circ + \angle R = 180^\circ$.
Solving for $\angle R,$ we find $\angle R = \boxed{120^\circ}$.
The answer is: 120
Below is a math problem. Provide a detailed, step-by-step solution.

### Problem:
In $\triangle PQR,$ the sum of $\angle P$ and $\angle Q$ is $60^\circ.$ What is the measure of $\angle R?$

### Answer:
