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° - 12°
= 28°
∠SUY
= 180° - 106°
= 74° (Angles on a straight line)
∠UYX
= 74° + 28°
= 102° (Exterior angle of a triangle)
(b)
∠STY
= 102° - 40°
= 62° (Exterior angle of a triangle)
Answer(s): (a) 102°; (b) 62°