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 = 50° and ∠SPT = 33°. Find
- ∠LPN
- ∠PRQ
(a)
∠LPT
= (180° - 50°) ÷ 2
= 65° (Isosceles triangle)
∠LPN
= 180° - 65°
= 115° (Angles on a straight line)
(b)
∠RPQ
= 65° - 33°
= 32°
∠PRQ
= (180° - 32°) ÷ 2
= 74 ° (Isosceles triangle)
Answer(s): (a) 115°; (b) 74°