The figure is not drawn to scale. GKLN is a parallelogram, FGN and GHN are isosceles triangles. NL//PV and ∠LUV= 108°. FK is straight line.
- Find ∠FNG.
- Find ∠KHN.
(a)
∠LUV = 108°
∠NST = 108° (Corresponding angles)
∠RSN
= 180° - 108°
= 72° (Angles on a straight line)
∠FNG
= 180° - 72° - 72°
= 36° (Isosceles triangle)
(b)
∠RSN = ∠FGN = 72° (Corresponding angles)
∠NGH
= 180° - 72°
= 108° (Angles on a straight line)
∠GHT
= (180° - 108°) ÷ 2
= 36° (Isosceles triangle)
∠KHN
= 180° - 36°
= 144° (Angles on a straight line)
Answer(s): (a) 36°; (b) 144°