In the figure, ∠DJN is a right-angled isosceles triangle. DN // FM , ∠LHG = 50°, ∠JLK = 40° and ∠GKH = 57°. Find
- ∠DNJ
- ∠HFM
- ∠KML
(a)
∠DNJ
= (180° - 90°) ÷ 2
= 90° ÷ 2
= 45° (Isosceles triangle)
(b)
∠JLE = 45° (Corresponding angles, ND//LE)
∠HLF
= ∠JLK + ∠JLE
= 40° + 45°
= 85°
∠HFM
= 180° - ∠LHG - ∠HLF
= 180° - 50° - 85°
= 45° (Angles sum of triangle)
(c)
∠KLM
= 180° - ∠HLF
= 180° - 85°
= 95°(Angles in a straight line)
∠MKL = ∠HKJ = 57° (Vertically opposite angles)
∠KML
= 180° - ∠MKL - ∠KLM
= 180° - 57° - 95°
= 28° (Angles sum of triangle)
Answer(s): (a) 45°; (b) 45°; (c) 28°
