Question

PLEASE HELP ASAP

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.
A) 1. Alternate Interior Angles Theorem; 2. Substitution Property
B) 1. Definition of Complementary Angles; 2. Substitution Property
C) 1. Definition of Supplementary Angles; 2. Transitive Property
D)1. Same-Side Interior Angles Theorem; 2. Transitive Property

Answer 1

To show that m∠AKL = 116°, you can use the Alternate Interior Angles Theorem. Therefore, the correct option is:

A) 1. Alternate Interior Angles Theorem; 2. Substitution Property

Explanation:

Here's how you can complete the proof:

By the Alternate Interior Angles Theorem, when two parallel lines are intersected by a transversal (in this case, line AB and line EF intersected by line KL), the alternate interior angles are congruent.

∠AKL is an alternate interior angle to some other angle (let's call it ∠XYZ).

Using the Substitution Property, you can substitute the value of ∠XYZ with the measure of ∠AKL.

Therefore, m∠AKL = m∠XYZ = 116°.

So, option A is the correct choice for the missing justifications.