In the figure, HLPS is a rectangle, PQST is a rhombus and LMNP is a parallelogram. ∠PQS = 80° and ∠NPQ = 92°.
- Find ∠KPL
- Find ∠PNM
(a)
∠STP = ∠SQP = 80°
∠TPS
= (180° - 80°) ÷ 2
= 100° ÷ 2
= 50° (Isosceles triangle)
∠KPL
= 90° - 50°
= 40°
(b)
∠LPN
= 360° - 92° - 90° - 50°
= 128° (Angles at a point)
∠MNP
= 180° - 128°
= 52° (Interior Angles, LP//MF)
Answer(s): (a) 40°; (b) 52°