*see attached pictures*

greg is constructing a fence that consists of parallel sides line ed and line fb. complete the proof to explain how he can show that m∠fac = 121° by finding the missing justifications.

answer choices:

a) 1. corresponding angles theorem; 2. definition of supplementary angles
b) 1. definition of supplementary angles; 2. corresponding angles theorem
c) 1. same-side interior angles theorem; 2. substitution property
d) 1. substitution property; 2. same-side interior angles theorem

C) 1. Same-Side Interior Angles Theorem; 2. Substitution Property

Step-by-step explanation:

Here, given that: Line ED is parallel to line FB

To show: ∠FAC = 121°

Now, here the given proof is:

ED II FB

∠ECG = 121°   ( Given)

∠ECG + ∠ECA = 180°   ( LINEAR PAIR POSTULATE)

∠FAC + ∠ECA = 180°   ( 1.Same-Side Interior Angles Theorem)

The same-side interior angle theorem states that when two lines that are parallel are intersected by a transversal line, the same-side interior angles that are formed are supplementary ( add up to 180°).

∠ECG + ∠ECA = ∠FAC + ∠ECA  (TRANSITIVE PROPERTY)

∠ECG  = ∠FAC   (SUBTRACTION PROPERTY)

∠FAC = ∠ECG    (SYMMETRY PROPERTY)

∠FAC  = 121°  (2. Substitution Property)

Hence, here the correct option is C) 1. Same-Side Interior Angles Theorem; 2. Substitution Property

explanation:

remove parenthesis:

=

apply rule

=

multiply fractions:

=

=

divide:

=

mordancy.