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 = 43° (Verticallly opposite angles)
∠VSY
= 43° - 13°
= 30°
∠SUY
= 180° - 102°
= 78° (Angles on a straight line)
∠UYX
= 78° + 30°
= 108° (Exterior angle of a triangle)
(b)
∠STY
= 108° - 43°
= 65° (Exterior angle of a triangle)
Answer(s): (a) 108°; (b) 65°