In the figure, O Is the centre of the circle and KR is parallel to LN. PS = PR, ∠OLK = 59° and ∠SRP = 50°. Find
- ∠NLT
- ∠LNP
(a)
OK = OL = Radius
∠KLO = ∠LKO = 59° (Isosceles triangle, OKB)
∠LOT
= 59° + 59°
= 118° (Exterior angle of a triangle)
OL = OT = Radius
∠OTL
= (180° - 118°) ÷ 2
= 62° ÷ 2
= 31°
∠NLT = 31° (Alternate angles, LN//KE)
(b)
PS = PR
∠PRS = ∠PSR = 50° (Isosceles triangle PRF)
∠RPS
= 180° - 50° - 50°
= 80°
∠TPN = ∠RPS = 80° (Vertically opposite angles)
∠LNP
= 180° - 80°
= 100° (Interior angles)
Answer(s): (a) 31°; (b) 100°
