In the figure, O Is the centre of the circle and FL is parallel to GH. KN = KL, ∠OGF = 59° and ∠NLK = 51°. Find
- ∠HGP
- ∠GHK
(a)
OF = OG = Radius
∠FGO = ∠GFO = 59° (Isosceles triangle, OFB)
∠GOP
= 59° + 59°
= 118° (Exterior angle of a triangle)
OG = OP = Radius
∠OPG
= (180° - 118°) ÷ 2
= 62° ÷ 2
= 31°
∠HGP = 31° (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) 31°; (b) 102°