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 = 36° (Verticallly opposite angles)
∠NKR
= 36° - 12°
= 24°
∠KMR
= 180° - 104°
= 76° (Angles on a straight line)
∠MRQ
= 76° + 24°
= 100° (Exterior angle of a triangle)
(b)
∠KLR
= 100° - 36°
= 64° (Exterior angle of a triangle)
Answer(s): (a) 100°; (b) 64°