State the missing reasons in this flow proof.

Given: angle 5 = 40, angle 2 = 140.
Prove: a is parallel to b.

Statements:
angle 5 = 40 a. ____________.
angle 2 = 140 b. _____________.
angle 5 and angle 2 are supplementary angles c.________.
Angle 5 and angle 2 are same-side interior angles d._________.
a is a parallel to b e._______

A. Given

B. Given
C. Consecutive interior angles theorem
D. Same-side interior angles theorem E. Proven

Im not sure if this is right, but this is what i put

A. Given

B: Given
C: Definition of supplementary angles
D: Definition of same side interior angles
E: converse of same side interior angles theorem

(a) and (b) are given.

(c) definition of supplementary angles
(d) can't tell without looking at the diagram, but
(c) and (d) imply (e)

Statements:

angle 5 = 40 a. __Reason: Given__.
angle 2 = 140 b. __Reason: Given__.
angle 5 and angle 2 are supplementary angles c. __Reason: Definition of supplementary angles__.
Angle 5 and angle 2 are same-side interior angles d. _________.
a is a parallel to b e. _________.

Missing reasons:

d. __Reason: Same-side interior angles that are supplementary imply parallel lines__.
e. __Reason: Corresponding angles formed by a transversal crossing parallel lines are congruent__.

To complete the flow proof, we need to fill in the missing reasons. Here is the completed flow proof:

Given: Angle 5 = 40, Angle 2 = 140.
Prove: a is parallel to b.

Statements:
1. Angle 5 = 40 a. Given.
2. Angle 2 = 140 b. Given.
3. Angle 5 and Angle 2 are supplementary angles c. ____________.
4. Angle 5 and Angle 2 are same-side interior angles d. ____________.
5. a is parallel to b e. ____________.

Now let's discuss how to fill in the missing reasons:

To fill in reason c, we need to use the definition of supplementary angles. Supplementary angles are two angles whose measures add up to 180 degrees. In this case, Angle 5 and Angle 2 are supplementary because they add up to 180 degrees.

Reason c: Definition of supplementary angles.

To fill in reason d, we need to use the property of same-side interior angles. Same-side interior angles are two interior angles that lie on the same side of the transversal and on the same side of the two parallel lines. In this case, Angle 5 and Angle 2 are same-side interior angles because they lie on the same side of the transversal (line a) and the same side of the two parallel lines (lines a and b).

Reason d: Property of same-side interior angles.

To fill in reason e, we need to use the converse of the Alternate Interior Angles Theorem. The converse states that if two lines are cut by a transversal and the alternate interior angles formed are congruent, then the lines are parallel. In this case, Angle 5 and Angle 2 are alternate interior angles that are congruent (40 degrees and 140 degrees). Therefore, line a is parallel to line b.

Reason e: Converse of the Alternate Interior Angles Theorem.

By completing the flow proof and providing the missing reasons, we have shown that a is parallel to b based on the given statements and the relevant geometric properties and theorems.