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° - 136°) ÷ 2
= 44° ÷ 2
= 22° (Isosceles triangle)
∠MPQ
= 60° - 22°
= 38° (Equilateral triangle)
(b)
∠MRQ
= 60° - 22°
= 38° (Equilateral triangle)
∠MQR
= 180° - 38° - 22°
= 120° (Angles sum of triangle)
∠MQP
= 360° - 136° - 120°
= 104° (Angles at a point)
∠NMP
= ∠MPQ
= 38° (Alternate angles)
∠NMR
= 60° + 38°
= 98°
Answer(s): (a) 38°; (b) 104°; (c) 98°
