In the figure, O Is the centre of the circle and KR is parallel to LN. PS = PR, ∠OLK = 53° and ∠SRP = 52°. Find
- ∠NLT
- ∠LNP
(a)
OK = OL = Radius
∠KLO = ∠LKO = 53° (Isosceles triangle, OKB)
∠LOT
= 53° + 53°
= 106° (Exterior angle of a triangle)
OL = OT = Radius
∠OTL
= (180° - 106°) ÷ 2
= 74° ÷ 2
= 37°
∠NLT = 37° (Alternate angles, LN//KE)
(b)
PS = PR
∠PRS = ∠PSR = 52° (Isosceles triangle PRF)
∠RPS
= 180° - 52° - 52°
= 76°
∠TPN = ∠RPS = 76° (Vertically opposite angles)
∠LNP
= 180° - 76°
= 104° (Interior angles)
Answer(s): (a) 37°; (b) 104°