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 = 38° (Verticallly opposite angles)
∠PLS
= 38° - 14°
= 24°
∠LNS
= 180° - 95°
= 85° (Angles on a straight line)
∠NSR
= 85° + 24°
= 109° (Exterior angle of a triangle)
(b)
∠LMS
= 109° - 38°
= 71° (Exterior angle of a triangle)
Answer(s): (a) 109°; (b) 71°