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° - 11°
= 31°
∠MPT
= 180° - 97°
= 83° (Angles on a straight line)
∠PTS
= 83° + 31°
= 114° (Exterior angle of a triangle)
(b)
∠MNT
= 114° - 42°
= 72° (Exterior angle of a triangle)
Answer(s): (a) 114°; (b) 72°