The figure is not drawn to scale. GKLN is a parallelogram, FGN and GHN are isosceles triangles. NL//PV and ∠LUV= 105°. FK is straight line.
- Find ∠FNG.
- Find ∠KHN.
(a)
∠LUV = 105°
∠NST = 105° (Corresponding angles)
∠RSN
= 180° - 105°
= 75° (Angles on a straight line)
∠FNG
= 180° - 75° - 75°
= 30° (Isosceles triangle)
(b)
∠RSN = ∠FGN = 75° (Corresponding angles)
∠NGH
= 180° - 75°
= 105° (Angles on a straight line)
∠GHT
= (180° - 105°) ÷ 2
= 37.5° (Isosceles triangle)
∠KHN
= 180° - 37.5°
= 142.5° (Angles on a straight line)
Answer(s): (a) 30°; (b) 142.5°