PSLE In the figure, CDHJ is a parallelogram and EFGH is a rhombus. JHG is a straight line. ∠DCJ = 57°, ∠HDE = 28° and ∠FEG = 34°.
- Find ∠DHE.
- Find ∠DEF.
(a)
∠DHJ
= ∠DCJ
= 57° (Parallelogram)
∠FGE
= ∠FEG
= 34° (Isosceles triangle)
∠EFG
= 180° - 34° - 34°
= 102° (Angles sum of triangle)
∠EHG
= ∠EFG
= 102° (Rhombus)
∠DHE
= 180° - 57° - 102°
= 21° (Angles on a straight line)
(b)
∠DEH
= 180° - 28° - 21°
= 131° (Angles sum of triangle)
∠GEH
= ∠FEG
= 34° (Rhombus)
∠DEF
= 360° - 131° - 34° - 34°
= 161° (Angles at a point)
Answer(s): (a) 21°; (b) 161°