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 ?
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To complete the proof, we need to solve the equation 12x = 180 and show that x = 15.
Proof:
1. Given: m<rst = 5x and m<uvw = 7x (angles rst and uvw are supplementary)
2. Definition of supplementary angles: m<rst + m<uvw = 180
3. Substitute the given values: 5x + 7x = 180
4. Solve the equation: 12x = 180
5. Divide both sides by 12: x = 180/12
6. Simplify: x = 15
Therefore, we have proven that x = 15.
To complete the proof, we need to solve the equation 12x = 180 and show that x = 15.
To solve the equation, we'll isolate x by dividing both sides by 12:
12x/12 = 180/12
x = 15
Since our equation simplifies to x = 15, we have proven that x = 15.
Therefore, the complete 2-column proof is as follows:
Statements:
1. Given: m<rst = 5x and m<uvw = 7x
2. <rst and <uvw are supplementary
Reasons:
1. <rst and <uvw are supplementary (Given)
2. m<rst + m<uvw = 180 (Definition of supplementary angles)
3. 5x + 7x = 180 (Substituting values from Given)
4. 12x = 180 (Combining like terms)
5. x = 15 (Dividing both sides by 12)
Therefore, x = 15.