The figure is not drawn to scale. MQSW is a parallelogram. PTV and NRU are triangles. ∠PTU = 76° and UNR = 52°. Find
- ∠NPT
- the sum of ∠NUR, ∠PKR and ∠RLT.
(a)
∠NPT
= 180° - 76°
= 104° (Interior angles, MQ//WS)
(b)
∠PKR = ∠NKL (Vertically opposite angles)
∠RLT = ∠ULK (Vertically opposite angles)
NULK is a quadrilateral.
∠NUR + ∠ULK + ∠NKL + 52° = 360° (Sum of angles in a quadrilateral)
∠NUR + ∠ULK + ∠NKL
= 360° - 52°
= 308°
Answer(s): (a) 104°; (b) 308°