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 = 45° and ∠SPT = 33°. Find
- ∠LPN
- ∠PRQ
(a)
∠LPT
= (180° - 45°) ÷ 2
= 67.5° (Isosceles triangle)
∠LPN
= 180° - 67.5°
= 112.5° (Angles on a straight line)
(b)
∠RPQ
= 67.5° - 33°
= 34.5°
∠PRQ
= (180° - 34.5°) ÷ 2
= 72.75 ° (Isosceles triangle)
Answer(s): (a) 112.5°; (b) 72.75°