In the figure, O Is the centre of the circle and CG is parallel to DE. FH = FG, ∠ODC = 57° and ∠HGF = 49°. Find
- ∠EDK
- ∠DEF
(a)
OC = OD = Radius
∠CDO = ∠DCO = 57° (Isosceles triangle, OCB)
∠DOK
= 57° + 57°
= 114° (Exterior angle of a triangle)
OD = OK = Radius
∠OKD
= (180° - 114°) ÷ 2
= 66° ÷ 2
= 33°
∠EDK = 33° (Alternate angles, DE//CE)
(b)
FH = FG
∠FGH = ∠FHG = 49° (Isosceles triangle FGF)
∠GFH
= 180° - 49° - 49°
= 82°
∠KFE = ∠GFH = 82° (Vertically opposite angles)
∠DEF
= 180° - 82°
= 98° (Interior angles)
Answer(s): (a) 33°; (b) 98°