The figure, not drawn to scale, O is the centre of the circle and HN // JM // KL. Find
- ∠GOK
- ∠GMO
(a)
∠NOJ
= 180° - 102°
= 78° (Interior angles, HN//JO)
∠OKM = ∠OMK = 34° (Isosceles triangle)
∠JOK
= 34° + 34°
= 68° (Exterior angle of a triangle)
∠GOK
= 78° + 68°
= 146°
(b)
∠MOK
= 180° - 34° -34°
= 112° (Isosceles triangle)
∠GOM
= 360° - 146° - 112°
= 102° (Angles at a point)
GO = OM = Radius
∠GMO
= (180° - 102°) ÷ 2
= 78° ÷ 2
= 39° (Isosceles triangle)
Answer(s): (a) 146°; (b) 39°