In the figure, O Is the centre of the circle and DH is parallel to EF. GK = GH, ∠OED = 57° and ∠KHG = 55°. Find
- ∠FEL
- ∠EFG
(a)
OD = OE = Radius
∠DEO = ∠EDO = 57° (Isosceles triangle, ODB)
∠EOL
= 57° + 57°
= 114° (Exterior angle of a triangle)
OE = OL = Radius
∠OLE
= (180° - 114°) ÷ 2
= 66° ÷ 2
= 33°
∠FEL = 33° (Alternate angles, EF//DE)
(b)
GK = GH
∠GHK = ∠GKH = 55° (Isosceles triangle GHF)
∠HGK
= 180° - 55° - 55°
= 70°
∠LGF = ∠HGK = 70° (Vertically opposite angles)
∠EFG
= 180° - 70°
= 110° (Interior angles)
Answer(s): (a) 33°; (b) 110°