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
1. Given that line AB is parallel to line EF
2. The sum of interior angles on the same side of the transversal is 180 degrees (Linear Pair Postulate)
3. The sum of angles KLF and BKL is equal to the sum of angles BKL and AKL
4. By subtracting angle BKL from both sides, we find that angle KLF is equal to angle AKL
5. By the symmetric property of equality, we can switch the order of the angles
6. Substituting the measure of angle KLF (which is given as 116 degrees) for angle AKL, we find that the measure of angle AKL is also 116 degrees.