The figure is not drawn to scale. GKLN is a parallelogram, FGN and GHN are isosceles triangles. NL//PV and ∠LUV= 119°. FK is straight line.
- Find ∠FNG.
- Find ∠KHN.
(a)
∠LUV = 119°
∠NST = 119° (Corresponding angles)
∠RSN
= 180° - 119°
= 61° (Angles on a straight line)
∠FNG
= 180° - 61° - 61°
= 58° (Isosceles triangle)
(b)
∠RSN = ∠FGN = 61° (Corresponding angles)
∠NGH
= 180° - 61°
= 119° (Angles on a straight line)
∠GHT
= (180° - 119°) ÷ 2
= 30.5° (Isosceles triangle)
∠KHN
= 180° - 30.5°
= 149.5° (Angles on a straight line)
Answer(s): (a) 58°; (b) 149.5°