Mathematics, 11.10.2020 09:01 Anderson0300
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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.
A. Corresponding Angles Theorem; 2. Definition of Supplementary Angles
B. Definition of Supplementary Angles; 2. Corresponding Angles Theorem
C. Same-Side Interior Angles Theorem; 2. Substitution Property
D. Substitution Property; 2. Same-Side Interior Angles Theorem
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