In the figure, HLPS is a rectangle, PQST is a rhombus and LMNP is a parallelogram. ∠PQS = 78° and ∠NPQ = 95°.
- Find ∠KPL
- Find ∠PNM
(a)
∠STP = ∠SQP = 78°
∠TPS
= (180° - 78°) ÷ 2
= 102° ÷ 2
= 51° (Isosceles triangle)
∠KPL
= 90° - 51°
= 39°
(b)
∠LPN
= 360° - 95° - 90° - 51°
= 124° (Angles at a point)
∠MNP
= 180° - 124°
= 56° (Interior Angles, LP//MF)
Answer(s): (a) 39°; (b) 56°