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 = 46° (Verticallly opposite angles)
∠NKR
= 46° - 10°
= 36°
∠KMR
= 180° - 101°
= 79° (Angles on a straight line)
∠MRQ
= 79° + 36°
= 115° (Exterior angle of a triangle)
(b)
∠KLR
= 115° - 46°
= 69° (Exterior angle of a triangle)
Answer(s): (a) 115°; (b) 69°