The figure is not drawn to scale. MPQR is a trapezium and MP // RQ. Given that MR = MN, ∠RMN = 76° and ∠MPQ = 99°.
- Find ∠PQR
- Find ∠MNR
- Find ∠NRQ
(a)
∠PQR
= 180° - 99°
= 81° (Interior angles, MP//RQ)
(b)
∠MNR
= (180° - 76°) ÷ 2
= 104° ÷ 2
= 52° (Isosceles triangle)
(c)
∠NRQ
= ∠MNR
= 52° (Alternate angles, MP//RQ)
Answer(s): (a) 81°; (b) 52°; (c) 52°