PSLE In the figure, PQUV is a parallelogram and RSTU is a rhombus. VUT is a straight line. ∠QPV = 56°, ∠UQR = 25° and ∠SRT = 33°.
- Find ∠QUR.
- Find ∠QRS.
(a)
∠QUV
= ∠QPV
= 56° (Parallelogram)
∠STR
= ∠SRT
= 33° (Isosceles triangle)
∠RST
= 180° - 33° - 33°
= 103° (Angles sum of triangle)
∠RUT
= ∠RST
= 103° (Rhombus)
∠QUR
= 180° - 56° - 103°
= 21° (Angles on a straight line)
(b)
∠QRU
= 180° - 25° - 21°
= 134° (Angles sum of triangle)
∠TRU
= ∠SRT
= 33° (Rhombus)
∠QRS
= 360° - 134° - 33° - 33°
= 160° (Angles at a point)
Answer(s): (a) 21°; (b) 160°