MNPQ is a square. RQP and NQQ are straight lines. NM = NR and ∠QNR = 15°. Find
- ∠NMR
- ∠QPR
.
(a)
∠MNQ = 45° (Right angle)
∠MNR
= ∠MNQ - ∠QNR
= 45° - 15°
= 30°
∠NMR
= (180° - ∠MNR) ÷ 2
= (180° - 30°) ÷ 2
= 150° ÷ 2
= 75° (Isosceles triangle)
(b)
NM = NR = NP
RNP is an isosceles triangle.
∠NRP = ∠NPR (Isosceles triangle)
∠NPR
= (180° - ∠QNP - ∠QNR) ÷ 2
= (180° - 45° -15°) ÷ 2
= 120° ÷ 2
= 60°
∠QPR
= ∠NPQ - ∠NPR
= 90° - 60°
= 30°
Answer(s): (a) 75°; (b) 30°
