The figure is not drawn to scale. GKLN is a parallelogram, FGN and GHN are isosceles triangles. NL//PV and ∠LUV= 104°. FK is straight line.
- Find ∠FNG.
- Find ∠KHN.
(a)
∠LUV = 104°
∠NST = 104° (Corresponding angles)
∠RSN
= 180° - 104°
= 76° (Angles on a straight line)
∠FNG
= 180° - 76° - 76°
= 28° (Isosceles triangle)
(b)
∠RSN = ∠FGN = 76° (Corresponding angles)
∠NGH
= 180° - 76°
= 104° (Angles on a straight line)
∠GHT
= (180° - 104°) ÷ 2
= 38° (Isosceles triangle)
∠KHN
= 180° - 38°
= 142° (Angles on a straight line)
Answer(s): (a) 28°; (b) 142°