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 = 39° (Verticallly opposite angles)
∠NKR
= 39° - 13°
= 26°
∠KMR
= 180° - 97°
= 83° (Angles on a straight line)
∠MRQ
= 83° + 26°
= 109° (Exterior angle of a triangle)
(b)
∠KLR
= 109° - 39°
= 70° (Exterior angle of a triangle)
Answer(s): (a) 109°; (b) 70°