The figure is not drawn to scale. CEFG is a parallelogram, BCG and CDG are isosceles triangles. GF//HR and ∠FPR= 114°. BE is straight line.
- Find ∠BGC.
- Find ∠EDG.
(a)
∠FPR = 114°
∠GLN = 114° (Corresponding angles)
∠KLG
= 180° - 114°
= 66° (Angles on a straight line)
∠BGC
= 180° - 66° - 66°
= 48° (Isosceles triangle)
(b)
∠KLG = ∠BCG = 66° (Corresponding angles)
∠GCD
= 180° - 66°
= 114° (Angles on a straight line)
∠CDN
= (180° - 114°) ÷ 2
= 33° (Isosceles triangle)
∠EDG
= 180° - 33°
= 147° (Angles on a straight line)
Answer(s): (a) 48°; (b) 147°