Does anyone know this? ive been stuck on it for a bit
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
1. alternate interior angles theorem; 2. definition of congruence
1. alternate exterior angles theorem; 2. substitution property
1. definition of congruence; 2. alternate interior angles theorem
1. substitution property; 2. alternate exterior angles theorem