From the given diagram we can see that ∠AFE and ∠BFD are vertical angles.
Using the Vertical Angles Theorem, we conclude that ∠A F E≅ ∠B F D. Additionally, notice that C is in the interior of ∠B F D. This will allow us to use the Angle Addition Postulate.
Statements
Reasons
1.
m∠A F E=180^(∘) and m∠B FC=42^(∘)
1.
Given
2.
∠A F E≅ ∠B F D
2.
Vertical Angles Theorem
3.
m∠A F E = m∠B F D
3.
Definition of Congruent Angles
4.
m∠B F D =m∠B FC + ∠C F D
4.
Angle Addition Postulate
5.
m∠A F E =m∠B FC + m∠C F D
5.
Substitution Method
6.
108^(∘) = 42^(∘) + m∠C F D
6.
Substitution Method
7.
m∠C F D = 66^(∘)
7.
Simplify
The angle measure that we have reached at the conclusion of our proof, m∠CFD = 66^(∘), corresponds to answer choice A.
