The figure is not drawn to scale. GKLN is a parallelogram, FGN and GHN are isosceles triangles. NL//PV and ∠LUV= 101°. FK is straight line.
- Find ∠FNG.
- Find ∠KHN.
(a)
∠LUV = 101°
∠NST = 101° (Corresponding angles)
∠RSN
= 180° - 101°
= 79° (Angles on a straight line)
∠FNG
= 180° - 79° - 79°
= 22° (Isosceles triangle)
(b)
∠RSN = ∠FGN = 79° (Corresponding angles)
∠NGH
= 180° - 79°
= 101° (Angles on a straight line)
∠GHT
= (180° - 101°) ÷ 2
= 39.5° (Isosceles triangle)
∠KHN
= 180° - 39.5°
= 140.5° (Angles on a straight line)
Answer(s): (a) 22°; (b) 140.5°