PSLE In the figure, STXY is a parallelogram and UVWX is a rhombus. YXW is a straight line. ∠TSY = 57°, ∠XTU = 29° and ∠VUW = 32°.
- Find ∠TXU.
- Find ∠TUV.
(a)
∠TXY
= ∠TSY
= 57° (Parallelogram)
∠VWU
= ∠VUW
= 32° (Isosceles triangle)
∠UVW
= 180° - 32° - 32°
= 104° (Angles sum of triangle)
∠UXW
= ∠UVW
= 104° (Rhombus)
∠TXU
= 180° - 57° - 104°
= 19° (Angles on a straight line)
(b)
∠TUX
= 180° - 29° - 19°
= 132° (Angles sum of triangle)
∠WUX
= ∠VUW
= 32° (Rhombus)
∠TUV
= 360° - 132° - 32° - 32°
= 164° (Angles at a point)
Answer(s): (a) 19°; (b) 164°