PSLE In the figure, PQUV is a parallelogram and RSTU is a rhombus. VUT is a straight line. ∠QPV = 59°, ∠UQR = 29° and ∠SRT = 33°.
- Find ∠QUR.
- Find ∠QRS.
(a)
∠QUV
= ∠QPV
= 59° (Parallelogram)
∠STR
= ∠SRT
= 33° (Isosceles triangle)
∠RST
= 180° - 33° - 33°
= 105° (Angles sum of triangle)
∠RUT
= ∠RST
= 105° (Rhombus)
∠QUR
= 180° - 59° - 105°
= 16° (Angles on a straight line)
(b)
∠QRU
= 180° - 29° - 16°
= 135° (Angles sum of triangle)
∠TRU
= ∠SRT
= 33° (Rhombus)
∠QRS
= 360° - 135° - 33° - 33°
= 159° (Angles at a point)
Answer(s): (a) 16°; (b) 159°