Mathematics

In the diagram above, ∠PTQ = ∠URP = 25° and XPU = 4URP. Calculate ∠USQ.

In the diagram above, ∠PTQ = ∠URP = 25° and XPU = 4URP. Calculate ∠USQ.

  • A.
    100o
  • B.
    120o
  • C.
    125o
  • D.
    130o
  • E.
    150o
Correct Answer: Option D
Explanation

Since < URP = 25°, then < XPU = 4 x 25° = 100°

(therefore) < TPQ = 180° – 100° = 80°

(therefore) < PQT = 180° – (80° + 25°) = 75°

< SQR = 75° – 25° = 50° (exterior angle = 2 opp interior angles)

(therefore) < USQ = 180° – 50° = 130°