In the figure, ∠DJN is a right-angled isosceles triangle. DN // FM , ∠LHG = 49°, ∠JLK = 41° and ∠GKH = 54°. Find
- ∠DNJ
- ∠HFM
- ∠KML
(a)
∠DNJ
= (180° - 90°) ÷ 2
= 90° ÷ 2
= 45° (Isosceles triangle)
(b)
∠JLE = 45° (Corresponding angles, ND//LE)
∠HLF
= ∠JLK + ∠JLE
= 41° + 45°
= 86°
∠HFM
= 180° - ∠LHG - ∠HLF
= 180° - 49° - 86°
= 45° (Angles sum of triangle)
(c)
∠KLM
= 180° - ∠HLF
= 180° - 86°
= 94°(Angles in a straight line)
∠MKL = ∠HKJ = 54° (Vertically opposite angles)
∠KML
= 180° - ∠MKL - ∠KLM
= 180° - 54° - 94°
= 32° (Angles sum of triangle)
Answer(s): (a) 45°; (b) 45°; (c) 32°
