Question

Line AB is parallel to EF. Transversal GJ crosses line AB at K and crosses line EF at L. The measure of angle ELJ is 120 degrees. Daniel is constructing a fence that consists of parallel sides line AB and line EF. Complete the proof to explain how he can show that m∠GKB = 120° by filling in the missing justifications:

a. 1. Alternate Interior Angles Theorem; 2. Definition of Congruence
b. 1. Alternate Exterior Angles Theorem; 2. Substitution Property
c. 1. Definition of Congruence; 2. Alternate Interior Angles Theorem
d. 1. Substitution Property; 2. Alternate Exterior Angles Theorem

Answer 1

The measure of angle m∠GKB is 120 degrees, as it is an alternate exterior angle to angle ELJ, which is also 120 degrees, based on the Alternate Exterior Angles Theorem and the Substitution Property. The correct answer is option b.

Step-by-step explanation:

To determine the measure of the angle m∠GKB, we can apply geometric theorems related to parallel lines and a transversal. Since line AB is parallel to line EF and GJ is a transversal crossing at points K and L, then angle ELJ and angle GKB are alternate exterior angles. According to the Alternate Exterior Angles Theorem, alternate exterior angles are equal when the lines are parallel and cut by a transversal, which directly provides us with the necessary angle measure.

Therefore, m∠GKB = 120° because m∠ELJ is given as 120°. The correct answer is option b: 1. Alternate Exterior Angles Theorem; 2. Substitution Property, where Substitution Property allows us to state that if one thing equals another, then one can be substituted for the other in any true statement.