Question

find the shortest side of δqrs, given that m∠q = 55°, m∠r = 80°, and m∠s = 45°.

Explanation:

Step1: Relate angles to opposite sides

In any triangle, the shortest side is opposite the smallest interior angle.

Step2: Identify smallest angle

Compare the angles: $m\angle Q=55^\circ$, $m\angle R=80^\circ$, $m\angle S=45^\circ$. The smallest angle is $\angle S = 45^\circ$.

Step3: Match angle to opposite side

The side opposite $\angle S$ in $\triangle QRS$ is $\overline{QR}$.

Answer:

$\overline{QR}$