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 = 45° (Verticallly opposite angles)
∠NKR
= 45° - 11°
= 34°
∠KMR
= 180° - 98°
= 82° (Angles on a straight line)
∠MRQ
= 82° + 34°
= 116° (Exterior angle of a triangle)
(b)
∠KLR
= 116° - 45°
= 71° (Exterior angle of a triangle)
Answer(s): (a) 116°; (b) 71°