m∠U = 58°
Step-by-step explanation:
The symbol (~) means triangle PQR is similar to triangle STU
When two triangles are similar, their three angles are the same
∠P = ∠S = 40°
∠Q = ∠T = 82°
∠R = ∠U
The sum of angles in a triangle = 180°
Using triangle PQR:
∠P + ∠Q + ∠R = 180°
40 + 82 + ∠R = 180°
122 + ∠R = 180
∠R = 180 - 122
∠R = 58°
Since ∠R = ∠U = 58°
Hence, m∠U = 58°