Question

find the longest side of (\triangle uvw).

Explanation:

Step1: Find the measure of $\angle{W}$

The sum of an interior angle and its adjacent exterior angle is $180^{\circ}$. So, $\angle{VWU}=180^{\circ}- 116^{\circ}=64^{\circ}$

Step2: Find the measure of $\angle{U}$

The sum of angles in a triangle is $180^{\circ}$. Let $\angle{U}=x$. Then $x + 60^{\circ}+64^{\circ}=180^{\circ}$. So, $x=180^{\circ}-(60^{\circ}+64^{\circ})=56^{\circ}$

Step3: Relate angles and sides

In a triangle, the larger angle is opposite the longer side. Since $64^{\circ}>60^{\circ}>56^{\circ}$, and $\angle{VWU} = 64^{\circ}$ is opposite side $UV$

Answer:

$UV$