The figure is not drawn to scale. MQSW is a parallelogram. PTV and NRU are triangles. ∠PTU = 83° and UNR = 54°. Find
- ∠NPT
- the sum of ∠NUR, ∠PKR and ∠RLT.
(a)
∠NPT
= 180° - 83°
= 97° (Interior angles, MQ//WS)
(b)
∠PKR = ∠NKL (Vertically opposite angles)
∠RLT = ∠ULK (Vertically opposite angles)
NULK is a quadrilateral.
∠NUR + ∠ULK + ∠NKL + 54° = 360° (Sum of angles in a quadrilateral)
∠NUR + ∠ULK + ∠NKL
= 360° - 54°
= 306°
Answer(s): (a) 97°; (b) 306°