In the figure, O Is the centre of the circle and FL is parallel to GH. KN = KL, ∠OGF = 60° and ∠NLK = 55°. Find
- ∠HGP
- ∠GHK
(a)
OF = OG = Radius
∠FGO = ∠GFO = 60° (Isosceles triangle, OFB)
∠GOP
= 60° + 60°
= 120° (Exterior angle of a triangle)
OG = OP = Radius
∠OPG
= (180° - 120°) ÷ 2
= 60° ÷ 2
= 30°
∠HGP = 30° (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) 30°; (b) 110°