Answer
$B$
Work Step by Step
In a triangle, the longest side lies opposite the largest angle. With this in mind, we can order the angles in $\triangle PQR$ according to their opposite sides.
Let's order the sides from least to greatest first:
$\overline{QR} < \overline{PQ} < \overline{RP}$
Now, let's match up the angle with the side opposite to it:
$\overline{QR}$ is opposite to $\angle P$
$\overline{PQ}$ is opposite to $\angle R$
$\overline{RP}$ is opposite to $\angle Q$
Option $A$ is not correct. We know nothing about the measures and cannot determine if two angles are less than another angle.
Option $B$ is correct. In our lineup, $\angle Q$ is the largest of the three angles.
Option $C$ cannot be correct because $m \angle R$ is less than $m \angle Q$ but greater than $m \angle P$.
Option $D$ is incorrect. $m \angle P < m \angle R$.
