The figure is not drawn to scale. MPQR is a trapezium and MP // RQ. Given that MR = MN, ∠RMN = 74° and ∠MPQ = 98°.
- Find ∠PQR
- Find ∠MNR
- Find ∠NRQ
(a)
∠PQR
= 180° - 98°
= 82° (Interior angles, MP//RQ)
(b)
∠MNR
= (180° - 74°) ÷ 2
= 106° ÷ 2
= 53° (Isosceles triangle)
(c)
∠NRQ
= ∠MNR
= 53° (Alternate angles, MP//RQ)
Answer(s): (a) 82°; (b) 53°; (c) 53°