LMNP is a quadrilateral and OLPN is a trapezium in which OL // PN and ∠MLP = 110°, ∠LPN = 122°, ∠MNP = 68° and PN = PL. Find
- ∠LMO
- ∠PLO
- ∠LNP.
(a)
∠LMO
= 360° - 122° -110° - 68°
= 60° (Sum of angles in a quadrilateral)
(b)
∠PLO
= 180° - 122°
= 58° (Interior angles, LO//PC)
(c)
∠LNP
= (180° - 122°) ÷ 2
= 58 ÷ 2
= 29° (Isosceles triangle)
Answer(s): (a) 60°; (b) 58°; (c) 29°