The two column proof has shown that m∠AKL = 116°
What is the complete two column proof?
The complete two column proof to show that m∠AKL = 116° is:
Statement Reason
m∠KLF = 116° Given
m∠KLF + m∠BKL = 180° Linear Pair Postulate
m∠BKL + m∠AKL = 180° Same-Side Interior Angles Theorem
m∠KLF + m∠BKL = m∠BKL + m∠AKL Transitive Property
m∠KLF = m∠AKL Subtraction Property
m∠AKL = m∠KLF Symmetric Property
m∠AKL = 116° Substitution Property
Complete question is:
ine 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