In the figure, O Is the centre of the circle and EK is parallel to FG. HL = HK, ∠OFE = 54° and ∠LKH = 49°. Find
- ∠GFN
- ∠FGH
(a)
OE = OF = Radius
∠EFO = ∠FEO = 54° (Isosceles triangle, OEB)
∠FON
= 54° + 54°
= 108° (Exterior angle of a triangle)
OF = ON = Radius
∠ONF
= (180° - 108°) ÷ 2
= 72° ÷ 2
= 36°
∠GFN = 36° (Alternate angles, FG//EE)
(b)
HL = HK
∠HKL = ∠HLK = 49° (Isosceles triangle HKF)
∠KHL
= 180° - 49° - 49°
= 82°
∠NHG = ∠KHL = 82° (Vertically opposite angles)
∠FGH
= 180° - 82°
= 98° (Interior angles)
Answer(s): (a) 36°; (b) 98°