Question

find the shortest side of δuvx.

Explanation:

Step1: Find angle at U

Angles on a straight line sum to \(180^\circ\). So, \(\angle VUX = 180^\circ - 118^\circ = 62^\circ\).

Step2: Find angle at V

Sum of angles in a triangle is \(180^\circ\). So, \(\angle V = 180^\circ - 62^\circ - 65^\circ = 53^\circ\).

Step3: Relate angles to sides

In a triangle, the shortest side is opposite the smallest angle. The angles are \(65^\circ\) (at X), \(62^\circ\) (at U), and \(53^\circ\) (at V). The smallest angle is \(53^\circ\) (at V), so the side opposite \(\angle V\) is \(UX\).

Answer:

\(UX\)