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 = 46° (Verticallly opposite angles)
∠PLS
= 46° - 10°
= 36°
∠LNS
= 180° - 105°
= 75° (Angles on a straight line)
∠NSR
= 75° + 36°
= 111° (Exterior angle of a triangle)
(b)
∠LMS
= 111° - 46°
= 65° (Exterior angle of a triangle)
Answer(s): (a) 111°; (b) 65°