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.

Question

StatementJustification
∥	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

Answer 1

Without the diagram it's a little challenging but I was able to reason out that KL is a transversal cutting across parallel lines AB and EF. Thus angles BKL and KLF are same-side interior angles and are supplementary. Angles BKL and AKL are a linear pair so they are also supplementary. You can then equate m∠KLF + m∠BKL to m∠BKL + m∠AKL by the transitive property. So the answer is:

1. Same-Side Interior Angles Theorem; 2. Transitive Property