PSLE In the figure, TUYZ is a parallelogram and VWXY is a rhombus. ZYX is a straight line. ∠UTZ = 56°, ∠YUV = 26° and ∠WVX = 33°.
- Find ∠UYV.
- Find ∠UVW.
(a)
∠UYZ
= ∠UTZ
= 56° (Parallelogram)
∠WXV
= ∠WVX
= 33° (Isosceles triangle)
∠VWX
= 180° - 33° - 33°
= 105° (Angles sum of triangle)
∠VYX
= ∠VWX
= 105° (Rhombus)
∠UYV
= 180° - 56° - 105°
= 19° (Angles on a straight line)
(b)
∠UVY
= 180° - 26° - 19°
= 135° (Angles sum of triangle)
∠XVY
= ∠WVX
= 33° (Rhombus)
∠UVW
= 360° - 135° - 33° - 33°
= 159° (Angles at a point)
Answer(s): (a) 19°; (b) 159°