PSLEMNPQ is a parallelogram, MPR is an equilateral triangle and PQ = QR.
- Find ∠MPQ.
- Find ∠PQM.
- Find ∠RMN.
(a)
PQ = QR
Triangle PQR is an isosceles triangle.
∠QPR
= (180° - 140°) ÷ 2
= 40° ÷ 2
= 20° (Isosceles triangle)
∠MPQ
= 60° - 20°
= 40° (Equilateral triangle)
(b)
∠MRQ
= 60° - 20°
= 40° (Equilateral triangle)
∠MQR
= 180° - 40° - 20°
= 120° (Angles sum of triangle)
∠MQP
= 360° - 140° - 120°
= 100° (Angles at a point)
∠NMP
= ∠MPQ
= 40° (Alternate angles)
∠NMR
= 60° + 40°
= 100°
Answer(s): (a) 40°; (b) 100°; (c) 100°