Question

find the longest side of $\triangle uvw$.

Explanation:

Step1: Sum triangle angles to 180°

$(c+60) + (c+50) + 5c = 180$

Step2: Simplify and solve for c

$7c + 110 = 180$
$7c = 70$
$c = 10$

Step3: Calculate each angle

$\angle V = 10+60 = 70^\circ$
$\angle U = 10+50 = 60^\circ$
$\angle W = 5\times10 = 50^\circ$

Step4: Match largest angle to opposite side

The largest angle is $\angle V = 70^\circ$, opposite side $UW$.

Answer:

The longest side is $\boldsymbol{UW}$