In the figure, DEFG is a parallelogram. O is the centre of the circle. Find
- ∠DGF
- ∠DEG
(a)
∠OEG = ∠EGO = 27° (Angle properties within a circle)
∠GOE
= 180° - 27° - 27°
= 126° (Angles sum of triangle)
∠ODE + ∠OED = ∠EOG (Exterior angle of a triangle)
∠ODE = ∠OED (Isosceles triangle, OD = OE)
∠ODE
= 126° ÷ 2
= 63° (Exterior angle of a triangle)
∠DGF
= 180° - 63°
= 117° (Interior angles)
(b)
∠DEG
= 180° - 63° - 27°
= 90° (Angle sum of triangles)
Answer(s): (a) 117°; (b) 90°