PSLE In the figure, PQUV is a parallelogram and RSTU is a rhombus. VUT is a straight line. ∠QPV = 57°, ∠UQR = 28° and ∠SRT = 32°.
- Find ∠QUR.
- Find ∠QRS.
(a)
∠QUV
= ∠QPV
= 57° (Parallelogram)
∠STR
= ∠SRT
= 32° (Isosceles triangle)
∠RST
= 180° - 32° - 32°
= 108° (Angles sum of triangle)
∠RUT
= ∠RST
= 108° (Rhombus)
∠QUR
= 180° - 57° - 108°
= 15° (Angles on a straight line)
(b)
∠QRU
= 180° - 28° - 15°
= 137° (Angles sum of triangle)
∠TRU
= ∠SRT
= 32° (Rhombus)
∠QRS
= 360° - 137° - 32° - 32°
= 159° (Angles at a point)
Answer(s): (a) 15°; (b) 159°