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

Answer:

1.Same-Side Interior Angles Theorem

2.Transitive property

Step-by-step explanation:

just took the test in FLVS and got it right! the other answer really explains it though :P

Answer 2

Answer:

1.Same-Side Interior Angles Theorem

2.Transitive property

Step-by-step explanation:

We are given that

$AB\parallel EF$

GJ is  a transversal line cut AB at K and intersect EF at L.

$m\angle KLF=116^{\circ}$

We have to fill the missing justification in given proof of $m\angle AKL=116^{\circ}$

Statement:$AB\parallel EF$

Reason: Given

Statement:$m\angle KLF=116^{\circ}$

Reason: Given

Statement:$m\angle KLF+m\angle BKL=180^{\circ}$

Reason:Same-Side Interior Angles Theorem

Statement:$m\angle BKL+m\angle AKL=180^{\circ}$

Reason: Linear pair

Statement: $m\angle KLF+m\angle BKL=m\angle BKL+m\angle AKL$

Reason:Transitive property

Statement:$m\angle KLF=m\angle AKL$

Reason:Subtraction property

Statement:$m\angle AKL=m\angle KLF$

Reason: Symmetric property

Statement:$m\angle AKL=116^{\circ}$

Reason: Substitution property