Question

find the shortest side of δqrs.

Explanation:

Step1: Find angle at R

Angles on a straight line sum to \(180^\circ\). So, \(\angle QRS = 180^\circ - 119^\circ = 61^\circ\).

Step2: Find angle at S

Sum of angles in a triangle is \(180^\circ\). Let \(\angle S = x\), then \(x + 66^\circ + 61^\circ = 180^\circ\). Solving, \(x = 180^\circ - 66^\circ - 61^\circ = 53^\circ\).

Step3: Relate angles to sides

In a triangle, the shortest side is opposite the smallest angle. Angles: \(\angle S = 53^\circ\), \(\angle R = 61^\circ\), \(\angle Q = 66^\circ\). Smallest angle is \(\angle S\), so side opposite (\(QR\)) is shortest.

Answer:

\(QR\)