In the figure, HJK and KLM are isosceles triangles where HK = JK and KL = KM. Given that LN, MQ and HS are straight lines, find
- ∠PTS
- ∠MNT
(a)
∠HJK = ∠JHK = ∠KLM = ∠KML (Isosceles triangle)
∠KML = ∠NMT = 42° (Verticallly opposite angles)
∠QMT
= 42° - 14°
= 28°
∠MPT
= 180° - 98°
= 82° (Angles on a straight line)
∠PTS
= 82° + 28°
= 110° (Exterior angle of a triangle)
(b)
∠MNT
= 110° - 42°
= 68° (Exterior angle of a triangle)
Answer(s): (a) 110°; (b) 68°