Answer
1. Given
2. Definition o fsupplementary angles
3. Angle Addition Postulate
4. Definition of angle bisectors
5. Substitution
6. Substitution
7. Division Property of Equality
8. Angle Addition Postulate
Work Step by Step
1. $\angle ABC$ is supp. to $\angle CBD$
2. $m\angle ABC +m\angle CBD=180^{\circ}$
3. $m\angle ABC = m\angle 1+m\angle2$
$m\angle CBD=m\angle3+m\angle4$
4. $m\angle 1=m\angle2$
$m\angle3=m\angle4$
5. $m\angle ABC = 2\times m\angle2$ (Substituting into statement (3.))
$m\angle CBD =2\times m\angle3$ (Substituting into statement (3.))
6. $2\times m\angle 2 + 2\times m\angle 3=180^{\circ}$ (Substituting into statement (2.))
7. $m\angle2+m\angle3=90^{\circ}$ ( Dividing both sides of the equation by 2 in statement (5.))
8. $\angle2+\angle3=\angle EBF$
Therefore $\angle EBF$ is a right angle.
