PSLE In the figure, TUYZ is a parallelogram and VWXY is a rhombus. ZYX is a straight line. ∠UTZ = 58°, ∠YUV = 29° and ∠WVX = 32°.
- Find ∠UYV.
- Find ∠UVW.
(a)
∠UYZ
= ∠UTZ
= 58° (Parallelogram)
∠WXV
= ∠WVX
= 32° (Isosceles triangle)
∠VWX
= 180° - 32° - 32°
= 108° (Angles sum of triangle)
∠VYX
= ∠VWX
= 108° (Rhombus)
∠UYV
= 180° - 58° - 108°
= 14° (Angles on a straight line)
(b)
∠UVY
= 180° - 29° - 14°
= 137° (Angles sum of triangle)
∠XVY
= ∠WVX
= 32° (Rhombus)
∠UVW
= 360° - 137° - 32° - 32°
= 159° (Angles at a point)
Answer(s): (a) 14°; (b) 159°