In the figure, ∠DJN is a right-angled isosceles triangle. DN // FM , ∠LHG = 47°, ∠JLK = 37° and ∠GKH = 56°. Find
- ∠DNJ
- ∠HFM
- ∠KML
(a)
∠DNJ
= (180° - 90°) ÷ 2
= 90° ÷ 2
= 45° (Isosceles triangle)
(b)
∠JLE = 45° (Corresponding angles, ND//LE)
∠HLF
= ∠JLK + ∠JLE
= 37° + 45°
= 82°
∠HFM
= 180° - ∠LHG - ∠HLF
= 180° - 47° - 82°
= 51° (Angles sum of triangle)
(c)
∠KLM
= 180° - ∠HLF
= 180° - 82°
= 98°(Angles in a straight line)
∠MKL = ∠HKJ = 56° (Vertically opposite angles)
∠KML
= 180° - ∠MKL - ∠KLM
= 180° - 56° - 98°
= 26° (Angles sum of triangle)
Answer(s): (a) 45°; (b) 51°; (c) 26°