In the figure, O Is the centre of the circle and FL is parallel to GH. KN = KL, ∠OGF = 54° and ∠NLK = 51°. Find
- ∠HGP
- ∠GHK
(a)
OF = OG = Radius
∠FGO = ∠GFO = 54° (Isosceles triangle, OFB)
∠GOP
= 54° + 54°
= 108° (Exterior angle of a triangle)
OG = OP = Radius
∠OPG
= (180° - 108°) ÷ 2
= 72° ÷ 2
= 36°
∠HGP = 36° (Alternate angles, GH//FE)
(b)
KN = KL
∠KLN = ∠KNL = 51° (Isosceles triangle KLF)
∠LKN
= 180° - 51° - 51°
= 78°
∠PKH = ∠LKN = 78° (Vertically opposite angles)
∠GHK
= 180° - 78°
= 102° (Interior angles)
Answer(s): (a) 36°; (b) 102°