The figure is not drawn to scale. MPQR is a trapezium and MP // RQ. Given that MR = MN, ∠RMN = 75° and ∠MPQ = 97°.
- Find ∠PQR
- Find ∠MNR
- Find ∠NRQ
(a)
∠PQR
= 180° - 97°
= 83° (Interior angles, MP//RQ)
(b)
∠MNR
= (180° - 75°) ÷ 2
= 105° ÷ 2
= 52.5° (Isosceles triangle)
(c)
∠NRQ
= ∠MNR
= 52.5° (Alternate angles, MP//RQ)
Answer(s): (a) 83°; (b) 52.5°; (c) 52.5°