Question

find the shortest side of $\triangle stu$.

Explanation:

Step1: Sum angles to 180°

$(c+23^\circ)+(c+19^\circ)+(c+12^\circ)=180^\circ$

Step2: Simplify the equation

$3c + 54^\circ = 180^\circ$

Step3: Solve for $c$

$3c=180^\circ-54^\circ=126^\circ$
$c=\frac{126^\circ}{3}=42^\circ$

Step4: Calculate each angle

$\angle S = 42^\circ+23^\circ=65^\circ$
$\angle T = 42^\circ+19^\circ=61^\circ$
$\angle U = 42^\circ+12^\circ=54^\circ$

Step5: Match smallest angle to side

The shortest side is opposite the smallest angle $\angle U$.

Answer:

$ST$