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Greg is constructing a fence that consists of parallel sides line ED and line FB. Complete the proof to explain how he can show that m∠FAC = 121° by finding the missing justifications.

Greg Is Constructing A Fence That Consists Of Parallel Sides Line ED And Line FB Complete The Proof To Explain How He Can Show That MFAC 121 By Finding The Miss class=

Answer :

Given:

Lines ED and FB are parallel

• m∠ECG = 121°

Let's complete the proof that shows that m∠FAC = 121° .

Here, we have the following:

• 1. m∠FAC + m∠ECA = 180°

Here, we can see that ∠FAC and ∠ECA are interior angles on the same side of the transversal. They can also be said to be opposite each other.

Since they are on the same side of the transversal, they are supplementary angles and supplementary angles sum up to 180 degrees.

Therefore, we have:

Statement Justification

m∠FAC + m∠ECA = 180° Definition of Supplementary Angles.

• 2. m∠FAC = 121°

Here, ∠ECG and ∠FAC can be said to be corresponding angles and corresponding angles are congruent.

Thus, we have:

m∠ECG ≅ m∠FAC = 121 degrees.

Statement Justification

m∠FAC = 121° Corresponding Angles Theorem.

• ANSWER:

1. Definition of Supplementary Angles; 2. Corresponding Angles Theorem

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