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McGraw Hill Integrated II, 2012
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McGraw Hill Integrated II, 2012 View details
4. Proving Angle Relationships
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Exercise 37 Page 307

Look for vertical angles. Then use the Angle Addition Postulate.

A

Practice makes perfect
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.

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arrow_right Exercises p.304-307
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Exercises 2 (Page 304)
Exercises 3 (Page 304)
Exercises 4 (Page 304)
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45 engineering
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