In the figure, LPSV is a rectangle, STVW is a rhombus and PQRS is a parallelogram. ∠STV = 74° and ∠RST = 97°.
- Find ∠NSP
- Find ∠SRQ
(a)
∠VWS = ∠VTS = 74°
∠WSV
= (180° - 74°) ÷ 2
= 106° ÷ 2
= 53° (Isosceles triangle)
∠NSP
= 90° - 53°
= 37°
(b)
∠PSR
= 360° - 97° - 90° - 53°
= 120° (Angles at a point)
∠QRS
= 180° - 120°
= 60° (Interior Angles, PS//QF)
Answer(s): (a) 37°; (b) 60°