In the figure, HLPS is a rectangle, PQST is a rhombus and LMNP is a parallelogram. ∠PQS = 76° and ∠NPQ = 97°.
- Find ∠KPL
- Find ∠PNM
(a)
∠STP = ∠SQP = 76°
∠TPS
= (180° - 76°) ÷ 2
= 104° ÷ 2
= 52° (Isosceles triangle)
∠KPL
= 90° - 52°
= 38°
(b)
∠LPN
= 360° - 97° - 90° - 52°
= 121° (Angles at a point)
∠MNP
= 180° - 121°
= 59° (Interior Angles, LP//MF)
Answer(s): (a) 38°; (b) 59°