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 = 42° (Verticallly opposite angles)
∠NKR
= 42° - 15°
= 27°
∠KMR
= 180° - 107°
= 73° (Angles on a straight line)
∠MRQ
= 73° + 27°
= 100° (Exterior angle of a triangle)
(b)
∠KLR
= 100° - 42°
= 58° (Exterior angle of a triangle)
Answer(s): (a) 100°; (b) 58°