In the figure, LPSV is a rectangle, STVW is a rhombus and PQRS is a parallelogram. ∠STV = 78° and ∠RST = 92°.
- Find ∠NSP
- Find ∠SRQ
(a)
∠VWS = ∠VTS = 78°
∠WSV
= (180° - 78°) ÷ 2
= 102° ÷ 2
= 51° (Isosceles triangle)
∠NSP
= 90° - 51°
= 39°
(b)
∠PSR
= 360° - 92° - 90° - 51°
= 127° (Angles at a point)
∠QRS
= 180° - 127°
= 53° (Interior Angles, PS//QF)
Answer(s): (a) 39°; (b) 53°