The figure is not drawn to scale. GKLN is a parallelogram, FGN and GHN are isosceles triangles. NL//PV and ∠LUV= 109°. FK is straight line.
- Find ∠FNG.
- Find ∠KHN.
(a)
∠LUV = 109°
∠NST = 109° (Corresponding angles)
∠RSN
= 180° - 109°
= 71° (Angles on a straight line)
∠FNG
= 180° - 71° - 71°
= 38° (Isosceles triangle)
(b)
∠RSN = ∠FGN = 71° (Corresponding angles)
∠NGH
= 180° - 71°
= 109° (Angles on a straight line)
∠GHT
= (180° - 109°) ÷ 2
= 35.5° (Isosceles triangle)
∠KHN
= 180° - 35.5°
= 144.5° (Angles on a straight line)
Answer(s): (a) 38°; (b) 144.5°