An image structure of two column geometric proof. The first column represents statements and consists of angles and operations, and the second column stands for reasons which include terminology from geometry such as 'Given', 'Definition of Supplementary angles', 'Substitution', 'Addition of like terms', and 'Division property of equality'. The diagram shows angle 'rst' and 'uvw' represented as arcs where arc 'rst' is labeled with 5x and 'uvw' is labeled with 7x. No text is included in the image to question or answer, it is strictly graphical illustration showing the entities mentioned.

Complete the 2 column proof.

Given m<rst = 5x and m<uvw = 7x
<rstand <uvw are supplementary.

Prove x=15

m<rst=5x and m<uvw=7x <rst and <uvw are supplementary given

m<rst + <uvw = 180 definition of supplementary angles

5x+7x = 180 ?

12x=180 ?

x=15 ?

My answer:

1. Given.
2. Definition of Supplementary angles.
3. Substitution.
4. Addition of like terms.
5. Division property of equality.

side note this is third hand

5x+7x=180 A. Property of linear pair
12x=180 B. Addition property
x=15 C. Division property

6. The quadratic formula.

Just kidding! The actual step is much simpler:

6. Simplification.

x = 15

No fancy quadratic formulas here, just good ol' division property of equality!

1. Given: m<rst = 5x and m<uvw = 7x

2. Given: <rst and <uvw are supplementary.
3. Definition of Supplementary angles: m<rst + m<uvw = 180
4. Substitution: 5x + 7x = 180
5. Addition of like terms: 12x = 180
6. Division property of equality: x = 15

To complete the 2 column proof, you need to apply the steps correctly in order to reach the conclusion that x equals 15. Let's go through the steps one by one:

1. Given.
This step acknowledges the information that is provided in the problem. In this case, it states that m<rst is equal to 5x and m<uvw is equal to 7x, and <rst and <uvw are supplementary.

2. Definition of Supplementary angles.
This step is stating the definition of supplementary angles, which is that the sum of their measures equals 180 degrees.

3. Substitution.
This step involves substituting the given values for m<rst and m<uvw into the equation from step 2. Therefore, 5x + 7x = 180.

4. Addition of like terms.
This step involves combining the like terms on the left side of the equation. So, 12x = 180.

5. Division property of equality.
This step applies the division property of equality, which allows you to divide both sides of the equation by the coefficient of x (which is 12 in this case). By dividing both sides of the equation by 12, you get x = 15.

Therefore, the conclusion is that x equals 15.

Write the statements supported by the reasons on the right side of the two-column proof.​

You're right in my opinion.