Question

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

Answer 1

The missing justifications are Same-Side Interior Angles Theorem and transitive property

What is an angle?

An angle is formed from the intersection of two lines. Types of angles are acute, obtuse, right angled.

m∠KLF = 116° (Given)

m∠KLF+ m∠BKL = 180° (Same-Side Interior Angles Theorem)

m∠BKL + m∠AKL = 180° (Linear Pair Postulate)

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)

The missing justifications are Same-Side Interior Angles Theorem and transitive property

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