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 = 46° and ∠SPT = 25°. Find
- ∠LPN
- ∠PRQ
(a)
∠LPT
= (180° - 46°) ÷ 2
= 67° (Isosceles triangle)
∠LPN
= 180° - 67°
= 113° (Angles on a straight line)
(b)
∠RPQ
= 67° - 25°
= 42°
∠PRQ
= (180° - 42°) ÷ 2
= 69 ° (Isosceles triangle)
Answer(s): (a) 113°; (b) 69°