In the figure, NPQ and QRS are isosceles triangles where NQ = PQ and QR = QS. Given that RT, SV and NX are straight lines, find
- ∠UYX
- ∠STY
(a)
∠NPQ = ∠PNQ = ∠QRS = ∠QSR (Isosceles triangle)
∠QSR = ∠TSY = 45° (Verticallly opposite angles)
∠VSY
= 45° - 16°
= 29°
∠SUY
= 180° - 103°
= 77° (Angles on a straight line)
∠UYX
= 77° + 29°
= 106° (Exterior angle of a triangle)
(b)
∠STY
= 106° - 45°
= 61° (Exterior angle of a triangle)
Answer(s): (a) 106°; (b) 61°