Question

find the shortest side of $\triangle qrs$.

Explanation:

Step1: Sum angles to 180°

$$60v + (v+62) + 57v = 180$$

Step2: Simplify the equation

$$60v + v + 62 + 57v = 180$$
$$118v + 62 = 180$$

Step3: Solve for v

$$118v = 180 - 62$$
$$118v = 118$$
$$v = 1$$

Step4: Calculate each angle

• $\angle R = 60(1) = 60^\circ$
• $\angle Q = 1 + 62 = 63^\circ$
• $\angle S = 57(1) = 57^\circ$

Step5: Match smallest angle to side

The smallest angle is $\angle S = 57^\circ$, which is opposite side $QR$.

Answer:

The shortest side is $\overline{QR}$