PSLENPQR is a parallelogram, NQS is an equilateral triangle and QR = RS.
- Find ∠NQR.
- Find ∠QRN.
- Find ∠SNP.
(a)
QR = RS
Triangle QRS is an isosceles triangle.
∠RQS
= (180° - 140°) ÷ 2
= 40° ÷ 2
= 20° (Isosceles triangle)
∠NQR
= 60° - 20°
= 40° (Equilateral triangle)
(b)
∠NSR
= 60° - 20°
= 40° (Equilateral triangle)
∠NRS
= 180° - 40° - 20°
= 120° (Angles sum of triangle)
∠NRQ
= 360° - 140° - 120°
= 100° (Angles at a point)
∠PNQ
= ∠NQR
= 40° (Alternate angles)
∠PNS
= 60° + 40°
= 100°
Answer(s): (a) 40°; (b) 100°; (c) 100°
