The figure, not drawn to scale, O is the centre of the circle and MS // NR // PQ. Find
- ∠LOP
- ∠LRO
(a)
∠SON
= 180° - 96°
= 84° (Interior angles, MS//NO)
∠OPR = ∠ORP = 28° (Isosceles triangle)
∠NOP
= 28° + 28°
= 56° (Exterior angle of a triangle)
∠LOP
= 84° + 56°
= 140°
(b)
∠ROP
= 180° - 28° -28°
= 124° (Isosceles triangle)
∠LOR
= 360° - 140° - 124°
= 96° (Angles at a point)
LO = OR = Radius
∠LRO
= (180° - 96°) ÷ 2
= 84° ÷ 2
= 42° (Isosceles triangle)
Answer(s): (a) 140°; (b) 42°