LMNP is a quadrilateral and OLPN is a trapezium in which OL // PN and ∠MLP = 112°, ∠LPN = 124°, ∠MNP = 64° and PN = PL. Find
- ∠LMO
- ∠PLO
- ∠LNP.
(a)
∠LMO
= 360° - 124° -112° - 64°
= 60° (Sum of angles in a quadrilateral)
(b)
∠PLO
= 180° - 124°
= 56° (Interior angles, LO//PC)
(c)
∠LNP
= (180° - 124°) ÷ 2
= 56 ÷ 2
= 28° (Isosceles triangle)
Answer(s): (a) 60°; (b) 56°; (c) 28°