2017 · Q96
In the figure given below, PQ is parallel to RS and PR is parallel to QS. If ∠ LPR = 35° and ∠ UST = 70°, then what is ∠ MPQ equal to ?
Elementary MathematicsGeometry: Lines, Angles and Triangles
- A55°
- B70°
- C75°
- D80°
Explanation
PQ ∥ RS and PR ∥ QS make PQRS a parallelogram. ∠QSR = ∠UST = 70° (vertically opposite); opposite angles of a parallelogram give ∠RPQ = ∠RSQ = 70°. On the straight line, ∠MPQ = 180° − ∠LPR − ∠RPQ = 180° − 35° − 70° = 75°: option C.