In the figure, O Is the centre of the circle and FL is parallel to GH. KN = KL, ∠OGF = 52° and ∠NLK = 49°. Find
- ∠HGP
- ∠GHK
(a)
OF = OG = Radius
∠FGO = ∠GFO = 52° (Isosceles triangle, OFB)
∠GOP
= 52° + 52°
= 104° (Exterior angle of a triangle)
OG = OP = Radius
∠OPG
= (180° - 104°) ÷ 2
= 76° ÷ 2
= 38°
∠HGP = 38° (Alternate angles, GH//FE)
(b)
KN = KL
∠KLN = ∠KNL = 49° (Isosceles triangle KLF)
∠LKN
= 180° - 49° - 49°
= 82°
∠PKH = ∠LKN = 82° (Vertically opposite angles)
∠GHK
= 180° - 82°
= 98° (Interior angles)
Answer(s): (a) 38°; (b) 98°
