Answer:
Step-by-step explanation:
[tex]\text{1. }\angle \text{CBE}=\angle\text{BCE}=2e^\circ\ \ \ \text{[Base angles of isosceles triangle are equal.]}\\[/tex]
[tex]\text{2. }\angle\text{ABC}=\angle\text{BCE}=2e^\circ\ \ \ [\text{Alternate angles are equal.}]\\\text{or, }g^\circ=2e^\circ[/tex]
[tex]3.\ \angle\text{ABF}=\angle \text{BFD}=120^\circ\ \ \ [\text{Alternate angles are equal.}]\\\text{or, }\angle \text{ABC}+\angle \text{CBE}+\angle \text{EBF}=120^\circ\\\text{or, }2e^o+2e^\circ+e^\circ=120^\circ\\\text{or, }5e^\circ=120^\circ\\\text{or, }e^\circ=24^\circ[/tex]
[tex]\text{4. }g^\circ=2e^\circ=2(24^\circ)=48^\circ[/tex]
[tex]\text{5. }\angle\text{EBF}+\angle\text{BEF}=\angle\text{BFD}\ \ \ [\text{An exterior angle of a triangle is equal to the}\\\text{}\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \text{sum of the opposite interior angles.]}\\\text{or, }e^\circ+f^\circ=120^\circ\\\text{or, }24^\circ+f^\circ=120^\circ\\\text{or, }f^\circ=96^\circ[/tex]
[tex]\bold{OR}[/tex]
[tex]\text{5. }\angle\text{CBE}+\angle\text{BCE}=\angle \text{BEF}\ \ \ [\text{An exterior angle of a triangle is equal to the}\\\text{}\qquad\qquad\qquad\qquad\qquad\qquad\qquad\text{sum of the opposite interior angles.}]\\\text{or, }2e^\circ+2e^\circ=f^\circ\\\text{or, }2(24^\circ)+2(24^\circ)=f^\circ\\\text{or, }f^\circ=96^\circ[/tex]
[tex]\bold{OR}[/tex]
[tex]\text{5. }\angle \text{ABE}=\angle \text{BEF}\ \ \ [\text{Alternate angles are equal.}]\\\text{or, }g^\circ+2e^\circ=f^\circ\\\text{or, }48^\circ+2(24^\circ)=f^\circ\\\text{or, }f^\circ=96^\circ[/tex]
