The figure is not drawn to scale. KNQU is a parallelogram. MRT and LPS are triangles. ∠MRS = 81° and SLP = 55°. Find
- ∠LMR
- the sum of ∠LSP, ∠MHP and ∠PJR.
(a)
∠LMR
= 180° - 81°
= 99° (Interior angles, KN//UQ)
(b)
∠MHP = ∠LHJ (Vertically opposite angles)
∠PJR = ∠SJH (Vertically opposite angles)
LSJH is a quadrilateral.
∠LSP + ∠SJH + ∠LHJ + 55° = 360° (Sum of angles in a quadrilateral)
∠LSP + ∠SJH + ∠LHJ
= 360° - 55°
= 305°
Answer(s): (a) 99°; (b) 305°