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 = 47° (Verticallly opposite angles)
∠VSY
= 47° - 16°
= 31°
∠SUY
= 180° - 99°
= 81° (Angles on a straight line)
∠UYX
= 81° + 31°
= 112° (Exterior angle of a triangle)
(b)
∠STY
= 112° - 47°
= 65° (Exterior angle of a triangle)
Answer(s): (a) 112°; (b) 65°