PSLE In the figure, STXY is a parallelogram and UVWX is a rhombus. YXW is a straight line. ∠TSY = 56°, ∠XTU = 28° and ∠VUW = 33°.
- Find ∠TXU.
- Find ∠TUV.
(a)
∠TXY
= ∠TSY
= 56° (Parallelogram)
∠VWU
= ∠VUW
= 33° (Isosceles triangle)
∠UVW
= 180° - 33° - 33°
= 104° (Angles sum of triangle)
∠UXW
= ∠UVW
= 104° (Rhombus)
∠TXU
= 180° - 56° - 104°
= 20° (Angles on a straight line)
(b)
∠TUX
= 180° - 28° - 20°
= 132° (Angles sum of triangle)
∠WUX
= ∠VUW
= 33° (Rhombus)
∠TUV
= 360° - 132° - 33° - 33°
= 162° (Angles at a point)
Answer(s): (a) 20°; (b) 162°