MNPQ is a square. LKP and NKQ are straight lines. NM = NL and ∠KNL = 15°. Find
- ∠NML
- ∠QPL
.
(a)
∠MNQ = 45° (Right angle)
∠MNL
= ∠MNQ - ∠KNL
= 45° - 15°
= 30°
∠NML
= (180° - ∠MNL) ÷ 2
= (180° - 30°) ÷ 2
= 150° ÷ 2
= 75° (Isosceles triangle)
(b)
NM = NL = NP
LNP is an isosceles triangle.
∠NLP = ∠NPL (Isosceles triangle)
∠NPL
= (180° - ∠QNP - ∠KNL) ÷ 2
= (180° - 45° -15°) ÷ 2
= 120° ÷ 2
= 60°
∠QPL
= ∠NPQ - ∠NPL
= 90° - 60°
= 30°
Answer(s): (a) 75°; (b) 30°
