Mathematics, 06.11.2020 22:50 DEVlN6070
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 mā GKB = 120Ā° by filling in the missing justifications.
Statement Justification
line AB ā„ line EF
mā ELJ = 120Ā° Given
mā ELJ + mā ELK = 180Ā° Linear Pair Postulate
mā BKL + mā GKB = 180Ā° Linear Pair Postulate
mā ELJ + mā ELK = mā BKL + mā GKB Transitive Property
ā ELK ā
ā BKL 1.
mā ELK = mā BKL 2.
mā ELJ + mā ELK = mā ELK + mā GKB Substitution Property
mā ELJ = mā GKB Subtraction Property
mā GKB = mā ELJ Symmetric Property
mā GKB = 120Ā° 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
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