Question

find the shortest side of $\triangle qst$.

Explanation:

Step1: Find ∠QTS

∠QTS and the 119° angle are supplementary, so:
$$180^\circ - 119^\circ = 61^\circ$$

Step2: Calculate ∠TQS

Sum of angles in a triangle is 180°:
$$180^\circ - 64^\circ - 61^\circ = 55^\circ$$

Step3: Match sides to angles

In a triangle, the shortest side is opposite the smallest angle. The smallest angle is ∠TQS = 55°, which is opposite side $ST$.

Answer:

$ST$