In the figure, O Is the centre of the circle and FL is parallel to GH. KN = KL, ∠OGF = 57° and ∠NLK = 55°. Find
- ∠HGP
- ∠GHK
(a)
OF = OG = Radius
∠FGO = ∠GFO = 57° (Isosceles triangle, OFB)
∠GOP
= 57° + 57°
= 114° (Exterior angle of a triangle)
OG = OP = Radius
∠OPG
= (180° - 114°) ÷ 2
= 66° ÷ 2
= 33°
∠HGP = 33° (Alternate angles, GH//FE)
(b)
KN = KL
∠KLN = ∠KNL = 55° (Isosceles triangle KLF)
∠LKN
= 180° - 55° - 55°
= 70°
∠PKH = ∠LKN = 70° (Vertically opposite angles)
∠GHK
= 180° - 70°
= 110° (Interior angles)
Answer(s): (a) 33°; (b) 110°