PSLE In the figure, STXY is a parallelogram and UVWX is a rhombus. YXW is a straight line. ∠TSY = 60°, ∠XTU = 28° and ∠VUW = 32°.
- Find ∠TXU.
- Find ∠TUV.
(a)
∠TXY
= ∠TSY
= 60° (Parallelogram)
∠VWU
= ∠VUW
= 32° (Isosceles triangle)
∠UVW
= 180° - 32° - 32°
= 105° (Angles sum of triangle)
∠UXW
= ∠UVW
= 105° (Rhombus)
∠TXU
= 180° - 60° - 105°
= 15° (Angles on a straight line)
(b)
∠TUX
= 180° - 28° - 15°
= 137° (Angles sum of triangle)
∠WUX
= ∠VUW
= 32° (Rhombus)
∠TUV
= 360° - 137° - 32° - 32°
= 159° (Angles at a point)
Answer(s): (a) 15°; (b) 159°