The figure is not drawn to scale. GKLN is a parallelogram, FGN and GHN are isosceles triangles. NL//PV and ∠LUV= 116°. FK is straight line.
- Find ∠FNG.
- Find ∠KHN.
(a)
∠LUV = 116°
∠NST = 116° (Corresponding angles)
∠RSN
= 180° - 116°
= 64° (Angles on a straight line)
∠FNG
= 180° - 64° - 64°
= 52° (Isosceles triangle)
(b)
∠RSN = ∠FGN = 64° (Corresponding angles)
∠NGH
= 180° - 64°
= 116° (Angles on a straight line)
∠GHT
= (180° - 116°) ÷ 2
= 32° (Isosceles triangle)
∠KHN
= 180° - 32°
= 148° (Angles on a straight line)
Answer(s): (a) 52°; (b) 148°