PSLE In the figure, TUYZ is a parallelogram and VWXY is a rhombus. ZYX is a straight line. ∠UTZ = 59°, ∠YUV = 29° and ∠WVX = 32°.
- Find ∠UYV.
- Find ∠UVW.
(a)
∠UYZ
= ∠UTZ
= 59° (Parallelogram)
∠WXV
= ∠WVX
= 32° (Isosceles triangle)
∠VWX
= 180° - 32° - 32°
= 106° (Angles sum of triangle)
∠VYX
= ∠VWX
= 106° (Rhombus)
∠UYV
= 180° - 59° - 106°
= 15° (Angles on a straight line)
(b)
∠UVY
= 180° - 29° - 15°
= 136° (Angles sum of triangle)
∠XVY
= ∠WVX
= 32° (Rhombus)
∠UVW
= 360° - 136° - 32° - 32°
= 160° (Angles at a point)
Answer(s): (a) 15°; (b) 160°