line ab is parallel to ef. transversal gj crosses line ab at k and crosses line ef at l. the measure of angle klf is 116 degrees.

missy is constructing a fence that consists of parallel sides line ab and line ef. complete the proof to explain how she can show that m∠akl = 116° by filling in the missing justifications.

statement justification

line ab ∥ line ef

m∠klf = 116° given

m∠klf+ m∠bkl = 180° 1.

m∠bkl + m∠akl = 180° linear pair postulate

m∠klf + m∠bkl = m∠bkl + m∠akl 2.

m∠klf = m∠akl subtraction property

m∠akl = m∠klf symmetric property

m∠akl = 116° substitution property

1. alternate interior angles theorem; 2. substitution property

1. definition of complementary angles; 2. substitution property

1. definition of supplementary angles; 2. transitive property

1. same-side interior angles theorem; 2. transitive property