The figure is not drawn to scale. MQSW is a parallelogram. PTV and NRU are triangles. ∠PTU = 79° and UNR = 55°. Find
- ∠NPT
- the sum of ∠NUR, ∠PKR and ∠RLT.
(a)
∠NPT
= 180° - 79°
= 101° (Interior angles, MQ//WS)
(b)
∠PKR = ∠NKL (Vertically opposite angles)
∠RLT = ∠ULK (Vertically opposite angles)
NULK is a quadrilateral.
∠NUR + ∠ULK + ∠NKL + 55° = 360° (Sum of angles in a quadrilateral)
∠NUR + ∠ULK + ∠NKL
= 360° - 55°
= 305°
Answer(s): (a) 101°; (b) 305°