MNPQ is a square. FEP and NEQ are straight lines. NM = NF and ∠ENF = 15°. Find
- ∠NMF
- ∠QPF
.
(a)
∠MNQ = 45° (Right angle)
∠MNF
= ∠MNQ - ∠ENF
= 45° - 15°
= 30°
∠NMF
= (180° - ∠MNF) ÷ 2
= (180° - 30°) ÷ 2
= 150° ÷ 2
= 75° (Isosceles triangle)
(b)
NM = NF = NP
FNP is an isosceles triangle.
∠NFP = ∠NPF (Isosceles triangle)
∠NPF
= (180° - ∠QNP - ∠ENF) ÷ 2
= (180° - 45° -15°) ÷ 2
= 120° ÷ 2
= 60°
∠QPF
= ∠NPQ - ∠NPF
= 90° - 60°
= 30°
Answer(s): (a) 75°; (b) 30°
