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° - 16°
= 31°
∠LNS
= 180° - 108°
= 72° (Angles on a straight line)
∠NSR
= 72° + 31°
= 103° (Exterior angle of a triangle)
(b)
∠LMS
= 103° - 47°
= 56° (Exterior angle of a triangle)
Answer(s): (a) 103°; (b) 56°