Question

find the longest side of $\triangle xyz$.

Explanation:

Step1: Sum angles to 180°

$(w+4^\circ)+(w+15^\circ)+(w-16^\circ)=180^\circ$

Step2: Simplify the equation

$3w + 3^\circ = 180^\circ$

Step3: Solve for $w$

$3w=177^\circ \implies w=59^\circ$

Step4: Calculate each angle

$\angle X = 59+4=63^\circ$, $\angle Y=59+15=74^\circ$, $\angle Z=59-16=43^\circ$

Step5: Match largest angle to side

Longest side opposes largest angle ($\angle Y$).

Answer:

The longest side is $\overline{XZ}$