In the adjoining figure $$\angle DAB$$ is $$8^\circ$$ more than $$\angle ADC$$, and $$\angle BCD$$ is $$8^\circ$$ less than $$\angle ADC$$. $$\angle FEB$$ is half of $$\angle FBE$$. Then the measure of $$\angle BFE$$ is

The figure marks $$\angle ADC = 92^\circ$$, so $$\angle DAB = 92^\circ + 8^\circ = 100^\circ$$ and $$\angle BCD = 92^\circ - 8^\circ = 84^\circ$$. The four angles of $$ABCD$$ add up to $$360^\circ$$, so $$\angle ABC = 360^\circ - 92^\circ - 100^\circ - 84^\circ = 84^\circ$$. As $$E$$ lies on $$AB$$ produced and $$F$$ lies on $$CB$$ produced, $$\angle FBE$$ is vertically opposite $$\angle ABC$$ and so equals $$84^\circ$$. Then $$\angle FEB = \frac{84^\circ}{2} = 42^\circ$$ and $$\angle BFE = 180^\circ - 84^\circ - 42^\circ = 54^\circ$$.