LMNP is a square. KJN and MJP are straight lines. ML = MK and ∠JMK = 15°. Find
- ∠MLK
- ∠PNK
.
(a)
∠LMP = 45° (Right angle)
∠LMK
= ∠LMP - ∠JMK
= 45° - 15°
= 30°
∠MLK
= (180° - ∠LMK) ÷ 2
= (180° - 30°) ÷ 2
= 150° ÷ 2
= 75° (Isosceles triangle)
(b)
ML = MK = MN
KMN is an isosceles triangle.
∠MKN = ∠MNK (Isosceles triangle)
∠MNK
= (180° - ∠PMN - ∠JMK) ÷ 2
= (180° - 45° -15°) ÷ 2
= 120° ÷ 2
= 60°
∠PNK
= ∠MNP - ∠MNK
= 90° - 60°
= 30°
Answer(s): (a) 75°; (b) 30°
