The figure is not drawn to scale. BDEF is a trapezium and BD // FE. Given that BF = BC, ∠FBC = 74° and ∠BDE = 99°.
- Find ∠DEF
- Find ∠BCF
- Find ∠CFE
(a)
∠DEF
= 180° - 99°
= 81° (Interior angles, BD//FE)
(b)
∠BCF
= (180° - 74°) ÷ 2
= 106° ÷ 2
= 53° (Isosceles triangle)
(c)
∠CFE
= ∠BCF
= 53° (Alternate angles, BD//FE)
Answer(s): (a) 81°; (b) 53°; (c) 53°