The figure is not drawn to scale. KNQU is a parallelogram. MRT and LPS are triangles. ∠MRS = 80° and SLP = 53°. Find
- ∠LMR
- the sum of ∠LSP, ∠MHP and ∠PJR.
(a)
∠LMR
= 180° - 80°
= 100° (Interior angles, KN//UQ)
(b)
∠MHP = ∠LHJ (Vertically opposite angles)
∠PJR = ∠SJH (Vertically opposite angles)
LSJH is a quadrilateral.
∠LSP + ∠SJH + ∠LHJ + 53° = 360° (Sum of angles in a quadrilateral)
∠LSP + ∠SJH + ∠LHJ
= 360° - 53°
= 307°
Answer(s): (a) 100°; (b) 307°