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 = 40° (Verticallly opposite angles)
∠VSY
= 40° - 11°
= 29°
∠SUY
= 180° - 102°
= 78° (Angles on a straight line)
∠UYX
= 78° + 29°
= 107° (Exterior angle of a triangle)
(b)
∠STY
= 107° - 40°
= 67° (Exterior angle of a triangle)
Answer(s): (a) 107°; (b) 67°
