In the figure, FGH and HJK are isosceles triangles where FH = GH and HJ = HK. Given that JL, KN and FQ are straight lines, find
- ∠MRQ
- ∠KLR
(a)
∠FGH = ∠GFH = ∠HJK = ∠HKJ (Isosceles triangle)
∠HKJ = ∠LKR = 38° (Verticallly opposite angles)
∠NKR
= 38° - 14°
= 24°
∠KMR
= 180° - 100°
= 80° (Angles on a straight line)
∠MRQ
= 80° + 24°
= 104° (Exterior angle of a triangle)
(b)
∠KLR
= 104° - 38°
= 66° (Exterior angle of a triangle)
Answer(s): (a) 104°; (b) 66°