In the figure, O Is the centre of the circle and KR is parallel to LN. PS = PR, ∠OLK = 52° and ∠SRP = 56°. Find
- ∠NLT
- ∠LNP
(a)
OK = OL = Radius
∠KLO = ∠LKO = 52° (Isosceles triangle, OKB)
∠LOT
= 52° + 52°
= 104° (Exterior angle of a triangle)
OL = OT = Radius
∠OTL
= (180° - 104°) ÷ 2
= 76° ÷ 2
= 38°
∠NLT = 38° (Alternate angles, LN//KE)
(b)
PS = PR
∠PRS = ∠PSR = 56° (Isosceles triangle PRF)
∠RPS
= 180° - 56° - 56°
= 68°
∠TPN = ∠RPS = 68° (Vertically opposite angles)
∠LNP
= 180° - 68°
= 112° (Interior angles)
Answer(s): (a) 38°; (b) 112°
