The figure is not drawn to scale. GKLN is a parallelogram, FGN and GHN are isosceles triangles. NL//PV and ∠LUV= 113°. FK is straight line.
- Find ∠FNG.
- Find ∠KHN.
(a)
∠LUV = 113°
∠NST = 113° (Corresponding angles)
∠RSN
= 180° - 113°
= 67° (Angles on a straight line)
∠FNG
= 180° - 67° - 67°
= 46° (Isosceles triangle)
(b)
∠RSN = ∠FGN = 67° (Corresponding angles)
∠NGH
= 180° - 67°
= 113° (Angles on a straight line)
∠GHT
= (180° - 113°) ÷ 2
= 33.5° (Isosceles triangle)
∠KHN
= 180° - 33.5°
= 146.5° (Angles on a straight line)
Answer(s): (a) 46°; (b) 146.5°