The figure is not drawn to scale. GKLN is a parallelogram, FGN and GHN are isosceles triangles. NL//PV and ∠LUV= 117°. FK is straight line.
- Find ∠FNG.
- Find ∠KHN.
(a)
∠LUV = 117°
∠NST = 117° (Corresponding angles)
∠RSN
= 180° - 117°
= 63° (Angles on a straight line)
∠FNG
= 180° - 63° - 63°
= 54° (Isosceles triangle)
(b)
∠RSN = ∠FGN = 63° (Corresponding angles)
∠NGH
= 180° - 63°
= 117° (Angles on a straight line)
∠GHT
= (180° - 117°) ÷ 2
= 31.5° (Isosceles triangle)
∠KHN
= 180° - 31.5°
= 148.5° (Angles on a straight line)
Answer(s): (a) 54°; (b) 148.5°