Question

Line ED is parallel to FB. Transversal GH crosses line ED at C and crosses line FB at A. The measure of angle ECG is 121 degrees.

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.



Statement Justification
line ED ∥ line FB
m∠ECG = 121° Given
m∠ECG + m∠ECA = 180° Linear Pair Postulate
m∠FAC + m∠ECA = 180° 1.
m∠ECG + m∠ECA = m∠FAC + m∠ECA Transitive Property
m∠ECG = m∠FAC Subtraction Property
m∠FAC = m∠ECG Symmetric Property
m∠FAC = 121° 2.
Group of answer choices

1. Same-Side Interior Angles Theorem; 2. Substitution Property

1. Substitution Property; 2. Same-Side Interior Angles Theorem

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

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

Answer 1

The proof shows that the angle ECG equals 121° and, using the Corresponding Angles Theorem and the properties of equality, demonstrates that angle FAC must also be 121°.

Step-by-step explanation:

The question involves proving that the measure of angle FAC (m∠FAC) is equal to 121° using parallel lines and the properties of angles created by a transversal. The proof presented is a series of logical steps that use geometric postulates and theorems to establish the equality of angles ECG and FAC.

m∠ECG + m∠ECA = 180° due to the Linear Pair Postulate, which states that adjacent angles that form a straight line sum to 180°.

m∠FAC + m∠ECA = 180°. This step uses the Corresponding Angles Theorem, which implies that when two parallel lines are cut by a transversal, the corresponding angles are congruent; hence m∠FAC is congruent to m∠ECG.

m∠ECG = m∠FAC by the Subtraction Property of equality, which allows the same quantity to be subtracted from both sides of an equation.

Finally, m∠FAC = m∠ECG by the Symmetric Property of equality, indicating that if one quantity equals another, then those two quantities can be interchanged.

m∠FAC = 121° by the Substitution Property, which permits the substitution of equal quantities in any expression.