In the figure, O Is the centre of the circle and KR is parallel to LN. PS = PR, ∠OLK = 54° and ∠SRP = 51°. Find
- ∠NLT
- ∠LNP
(a)
OK = OL = Radius
∠KLO = ∠LKO = 54° (Isosceles triangle, OKB)
∠LOT
= 54° + 54°
= 108° (Exterior angle of a triangle)
OL = OT = Radius
∠OTL
= (180° - 108°) ÷ 2
= 72° ÷ 2
= 36°
∠NLT = 36° (Alternate angles, LN//KE)
(b)
PS = PR
∠PRS = ∠PSR = 51° (Isosceles triangle PRF)
∠RPS
= 180° - 51° - 51°
= 78°
∠TPN = ∠RPS = 78° (Vertically opposite angles)
∠LNP
= 180° - 78°
= 102° (Interior angles)
Answer(s): (a) 36°; (b) 102°