In the figure, GHJ and JKL are isosceles triangles where GJ = HJ and JK = JL. Given that KM, LP and GR are straight lines, find
- ∠NSR
- ∠LMS
(a)
∠GHJ = ∠HGJ = ∠JKL = ∠JLK (Isosceles triangle)
∠JLK = ∠MLS = 47° (Verticallly opposite angles)
∠PLS
= 47° - 11°
= 36°
∠LNS
= 180° - 110°
= 70° (Angles on a straight line)
∠NSR
= 70° + 36°
= 106° (Exterior angle of a triangle)
(b)
∠LMS
= 106° - 47°
= 59° (Exterior angle of a triangle)
Answer(s): (a) 106°; (b) 59°