KLMN is a square. JHM and LHN are straight lines. LK = LJ and ∠HLJ = 11°. Find
- ∠LKJ
- ∠NMJ
.
(a)
∠KLN = 45° (Right angle)
∠KLJ
= ∠KLN - ∠HLJ
= 45° - 11°
= 34°
∠LKJ
= (180° - ∠KLJ) ÷ 2
= (180° - 34°) ÷ 2
= 146° ÷ 2
= 73° (Isosceles triangle)
(b)
LK = LJ = LM
JLM is an isosceles triangle.
∠LJM = ∠LMJ (Isosceles triangle)
∠LMJ
= (180° - ∠NLM - ∠HLJ) ÷ 2
= (180° - 45° -11°) ÷ 2
= 124° ÷ 2
= 62°
∠NMJ
= ∠LMN - ∠LMJ
= 90° - 62°
= 28°
Answer(s): (a) 73°; (b) 28°
