The figure is not drawn to scale. GKLN is a parallelogram, FGN and GHN are isosceles triangles. NL//PV and ∠LUV= 111°. FK is straight line.
- Find ∠FNG.
- Find ∠KHN.
(a)
∠LUV = 111°
∠NST = 111° (Corresponding angles)
∠RSN
= 180° - 111°
= 69° (Angles on a straight line)
∠FNG
= 180° - 69° - 69°
= 42° (Isosceles triangle)
(b)
∠RSN = ∠FGN = 69° (Corresponding angles)
∠NGH
= 180° - 69°
= 111° (Angles on a straight line)
∠GHT
= (180° - 111°) ÷ 2
= 34.5° (Isosceles triangle)
∠KHN
= 180° - 34.5°
= 145.5° (Angles on a straight line)
Answer(s): (a) 42°; (b) 145.5°