In the figure, LPSV is a rectangle, STVW is a rhombus and PQRS is a parallelogram. ∠STV = 72° and ∠RST = 91°.
- Find ∠NSP
- Find ∠SRQ
(a)
∠VWS = ∠VTS = 72°
∠WSV
= (180° - 72°) ÷ 2
= 108° ÷ 2
= 54° (Isosceles triangle)
∠NSP
= 90° - 54°
= 36°
(b)
∠PSR
= 360° - 91° - 90° - 54°
= 125° (Angles at a point)
∠QRS
= 180° - 125°
= 55° (Interior Angles, PS//QF)
Answer(s): (a) 36°; (b) 55°