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 = 45° (Verticallly opposite angles)
∠QMT
= 45° - 16°
= 29°
∠MPT
= 180° - 96°
= 84° (Angles on a straight line)
∠PTS
= 84° + 29°
= 113° (Exterior angle of a triangle)
(b)
∠MNT
= 113° - 45°
= 68° (Exterior angle of a triangle)
Answer(s): (a) 113°; (b) 68°