The figure is not drawn to scale. JKN is an equilateral triangle and MKL is an isosceles triangle. LKJ and KMP are straight lines and LJ//PN. ∠NKP = 90° and ∠MNK = 60°.
- Find ∠LKP.
- Find ∠KML.
- Find ∠NMP.
(a)
∠NKJ = 60° (Equilateral triangle JKY)
∠NKP = 90°
∠MNK = 60°
∠LKP
= 180° - ∠NKP - ∠NKJ
= 180° - 90° - 60°
= 30° (Angles on a straight line)
(b)
∠KML
= (180° - ∠LKP ÷ 2
= (180° - 30°) ÷ 2
= 150° ÷ 2
= 75° (Isosceles triangle)
(c)
∠NMK
= 180° - ∠NKP - ∠MNK
= 180° - 90° - 60°
= 30°
∠NMP
= 180° - ∠NMK
= 180° - 30°
= 150° (Angles on a straight line)
Answer(s): (a) 30°; (b) 75°; (c) 150°
