In the figure, O Is the centre of the circle and EK is parallel to FG. HL = HK, ∠OFE = 53° and ∠LKH = 55°. Find
- ∠GFN
- ∠FGH
(a)
OE = OF = Radius
∠EFO = ∠FEO = 53° (Isosceles triangle, OEB)
∠FON
= 53° + 53°
= 106° (Exterior angle of a triangle)
OF = ON = Radius
∠ONF
= (180° - 106°) ÷ 2
= 74° ÷ 2
= 37°
∠GFN = 37° (Alternate angles, FG//EE)
(b)
HL = HK
∠HKL = ∠HLK = 55° (Isosceles triangle HKF)
∠KHL
= 180° - 55° - 55°
= 70°
∠NHG = ∠KHL = 70° (Vertically opposite angles)
∠FGH
= 180° - 70°
= 110° (Interior angles)
Answer(s): (a) 37°; (b) 110°