PSLE In the figure, TUYZ is a parallelogram and VWXY is a rhombus. ZYX is a straight line. ∠UTZ = 56°, ∠YUV = 29° and ∠WVX = 34°.
- Find ∠UYV.
- Find ∠UVW.
(a)
∠UYZ
= ∠UTZ
= 56° (Parallelogram)
∠WXV
= ∠WVX
= 34° (Isosceles triangle)
∠VWX
= 180° - 34° - 34°
= 106° (Angles sum of triangle)
∠VYX
= ∠VWX
= 106° (Rhombus)
∠UYV
= 180° - 56° - 106°
= 18° (Angles on a straight line)
(b)
∠UVY
= 180° - 29° - 18°
= 133° (Angles sum of triangle)
∠XVY
= ∠WVX
= 34° (Rhombus)
∠UVW
= 360° - 133° - 34° - 34°
= 159° (Angles at a point)
Answer(s): (a) 18°; (b) 159°