Question

find the shortest side of $\triangle rtu$.

Explanation:

Step1: Find ∠TUS supplementary angle

∠TUS and ∠TUR are supplementary, so:
$\angle TUR = 180^\circ - 120^\circ = 60^\circ$

Step2: Calculate ∠RTU

Sum of angles in $\triangle RTU$ is $180^\circ$:
$\angle RTU = 180^\circ - 55^\circ - 60^\circ = 65^\circ$

Step3: Match angles to opposite sides

In a triangle, the shortest side is opposite the smallest angle:

• Smallest angle: $\angle R = 55^\circ$
• Side opposite $\angle R$: $TU$

Answer:

The shortest side of $\triangle RTU$ is $\boldsymbol{TU}$