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° - 12°
= 35°
∠LNS
= 180° - 96°
= 84° (Angles on a straight line)
∠NSR
= 84° + 35°
= 119° (Exterior angle of a triangle)
(b)
∠LMS
= 119° - 47°
= 72° (Exterior angle of a triangle)
Answer(s): (a) 119°; (b) 72°