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 = 44° (Verticallly opposite angles)
∠NKR
= 44° - 14°
= 30°
∠KMR
= 180° - 107°
= 73° (Angles on a straight line)
∠MRQ
= 73° + 30°
= 103° (Exterior angle of a triangle)
(b)
∠KLR
= 103° - 44°
= 59° (Exterior angle of a triangle)
Answer(s): (a) 103°; (b) 59°