Line AB is parallel to EF. Transversal GJ crosses line AB at K and crosses line EF at L. The measure of angle ELJ is 120 degrees
. Daniel is constructing a fence that consists of parallel sides line AB and line EF. Complete the proof to explain how he can show that m∠GKB = 120° by filling in the missing justifications.
Statement Justification
line AB ∥ line EF
m∠ELJ = 120° Given
m∠ELJ + m∠ELK = 180° Linear Pair Postulate
m∠BKL + m∠GKB = 180° Linear Pair Postulate
m∠ELJ + m∠ELK = m∠BKL + m∠GKB Transitive Property
∠ELK ≅ ∠BKL 1.
m∠ELK = m∠BKL 2.
m∠ELJ + m∠ELK = m∠ELK + m∠GKB Substitution Property
m∠ELJ = m∠GKB Subtraction Property
m∠GKB = m∠ELJ Symmetric Property
m∠GKB = 120° Substitution
A 1. Alternate Interior Angles Theorem; 2. Definition of Congruence
B 1. Alternate Exterior Angles Theorem; 2. Substitution Property
C 1. Definition of Congruence; 2. Alternate Interior Angles Theorem
D 1. Substitution Property; 2. Alternate Exterior Angles Theorem
