In the figure, LMNP is a trapezium and LPQT is a rhombus. LP is parallel to MN and PQ = PR. TPN and PSR are straight lines. ∠PLT = 48° and ∠SPT = 29°. Find
- ∠LPN
- ∠PRQ
(a)
∠LPT
= (180° - 48°) ÷ 2
= 66° (Isosceles triangle)
∠LPN
= 180° - 66°
= 114° (Angles on a straight line)
(b)
∠RPQ
= 66° - 29°
= 37°
∠PRQ
= (180° - 37°) ÷ 2
= 71.5 ° (Isosceles triangle)
Answer(s): (a) 114°; (b) 71.5°