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 = 46° (Verticallly opposite angles)
∠VSY
= 46° - 12°
= 34°
∠SUY
= 180° - 97°
= 83° (Angles on a straight line)
∠UYX
= 83° + 34°
= 117° (Exterior angle of a triangle)
(b)
∠STY
= 117° - 46°
= 71° (Exterior angle of a triangle)
Answer(s): (a) 117°; (b) 71°