Question

list the side lengths of δtuv in order from shortest to longest.

Explanation:

Step1: Find ∠TVU (supplementary angle)

$\angle TVU = 180^\circ - 139^\circ = 41^\circ$

Step2: Calculate ∠U (triangle angle sum)

$\angle U = 180^\circ - 75^\circ - 41^\circ = 64^\circ$

Step3: Match sides to opposite angles

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

• Smallest angle ($41^\circ$) → Opposite side $TU$
• Middle angle ($64^\circ$) → Opposite side $TV$
• Largest angle ($75^\circ$) → Opposite side $UV$

Answer:

$TU < UV < TV$