The figure, not drawn to scale, O is the centre of the circle and MS // NR // PQ. Find
- ∠LOP
- ∠LRO
(a)
∠SON
= 180° - 100°
= 80° (Interior angles, MS//NO)
∠OPR = ∠ORP = 28° (Isosceles triangle)
∠NOP
= 28° + 28°
= 56° (Exterior angle of a triangle)
∠LOP
= 80° + 56°
= 136°
(b)
∠ROP
= 180° - 28° -28°
= 124° (Isosceles triangle)
∠LOR
= 360° - 136° - 124°
= 100° (Angles at a point)
LO = OR = Radius
∠LRO
= (180° - 100°) ÷ 2
= 80° ÷ 2
= 40° (Isosceles triangle)
Answer(s): (a) 136°; (b) 40°