Answer
$H$
Work Step by Step
The largest angle lies opposite to the longest side.
We have the measures of two angles in a triangle, so we need to find the measure of the third angle. We can accomplish this by using the triangle sum theorem, which states that the sum of the measures of the interior angles of a triangle must equal $180^{\circ}$.
$m \angle T = 180 - (72 + 55)$
Evaluate what is in parentheses first:
$m \angle T = 180 - (127)$
Subtract to solve:
$m \angle T = 53^{\circ}$
Now, let's figure out which side lies opposite to which angle:
$\angle H$ lies opposite to $\overline{TQ}$.
$\angle T$ lies opposite to $\overline{HQ}$.
$\angle Q$ lies opposite to $\overline{HT}$.
Let's put the angles in order from least to greatest first:
$\angle T$ < $\angle Q$ < $\angle H$
Now, we can order the sides by matching them up with the angles that are opposite to them:
$\overline{HQ}$ < $\overline{HT}$ < $\overline{TQ}$
The answer is option $H$.
