PSLE In the figure, ABFG is a parallelogram and CDEF is a rhombus. GFE is a straight line. ∠BAG = 57°, ∠FBC = 28° and ∠DCE = 34°.
- Find ∠BFC.
- Find ∠BCD.
(a)
∠BFG
= ∠BAG
= 57° (Parallelogram)
∠DEC
= ∠DCE
= 34° (Isosceles triangle)
∠CDE
= 180° - 34° - 34°
= 104° (Angles sum of triangle)
∠CFE
= ∠CDE
= 104° (Rhombus)
∠BFC
= 180° - 57° - 104°
= 19° (Angles on a straight line)
(b)
∠BCF
= 180° - 28° - 19°
= 133° (Angles sum of triangle)
∠ECF
= ∠DCE
= 34° (Rhombus)
∠BCD
= 360° - 133° - 34° - 34°
= 159° (Angles at a point)
Answer(s): (a) 19°; (b) 159°