In the figure, HLPS is a rectangle, PQST is a rhombus and LMNP is a parallelogram. ∠PQS = 72° and ∠NPQ = 91°.
- Find ∠KPL
- Find ∠PNM
(a)
∠STP = ∠SQP = 72°
∠TPS
= (180° - 72°) ÷ 2
= 108° ÷ 2
= 54° (Isosceles triangle)
∠KPL
= 90° - 54°
= 36°
(b)
∠LPN
= 360° - 91° - 90° - 54°
= 125° (Angles at a point)
∠MNP
= 180° - 125°
= 55° (Interior Angles, LP//MF)
Answer(s): (a) 36°; (b) 55°