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° - 138°) ÷ 2
= 42° ÷ 2
= 21° (Isosceles triangle)
∠NQR
= 60° - 21°
= 39° (Equilateral triangle)
(b)
∠NSR
= 60° - 21°
= 39° (Equilateral triangle)
∠NRS
= 180° - 39° - 21°
= 120° (Angles sum of triangle)
∠NRQ
= 360° - 138° - 120°
= 102° (Angles at a point)
∠PNQ
= ∠NQR
= 39° (Alternate angles)
∠PNS
= 60° + 39°
= 99°
Answer(s): (a) 39°; (b) 102°; (c) 99°