Question

assignment
find the value of x that makes lines u and v parallel. also state which postulate or theorem justifies your answer.
1)
2)
3)
4)

Explanation:

1. Problem 1:

• Explanation:
• Step1: Use the consecutive - interior angles theorem
• If lines \(u\) and \(v\) are parallel, then \((x + 63)+(x + 123)=180\) (consecutive - interior angles are supplementary).
• Expand the left - hand side: \(x+63+x + 123=180\), which simplifies to \(2x+186 = 180\).
• Step2: Solve for \(x\)
• Subtract 186 from both sides: \(2x=180 - 186=-6\).
• Divide both sides by 2: \(x=-3\).
• Answer: \(x=-3\), justified by the consecutive - interior angles theorem.

1. Problem 2:

• Explanation:
• Step1: Use the corresponding angles theorem
• If lines \(u\) and \(v\) are parallel, then \(6x + 13=79\) (corresponding angles are equal).
• Step2: Solve for \(x\)
• Subtract 13 from both sides: \(6x=79 - 13 = 66\).
• Divide both sides by 6: \(x = 11\).
• Answer: \(x = 11\), justified by the corresponding angles theorem.

1. Problem 3:

• Explanation:
• Step1: Use the alternate - interior angles theorem
• If lines \(u\) and \(v\) are parallel, then \(7x+17=-1 + 9x\) (alternate - interior angles are equal).
• Step2: Solve for \(x\)
• Subtract \(7x\) from both sides: \(17=-1+9x - 7x\).
• Simplify to \(17=-1 + 2x\).
• Add 1 to both sides: \(18=2x\).
• Divide both sides by 2: \(x = 9\).
• Answer: \(x = 9\), justified by the alternate - interior angles theorem.

1. Problem 4:

• Explanation:
• Step1: Use the corresponding angles theorem
• If lines \(u\) and \(v\) are parallel, then \(13+6x=7x + 6\) (corresponding angles are equal).
• Step2: Solve for \(x\)
• Subtract \(6x\) from both sides: \(13=7x+6 - 6x\).
• Simplify to \(13=x + 6\).
• Subtract 6 from both sides: \(x=7\).
• Answer: \(x = 7\), justified by the corresponding angles theorem.

Answer:

1. Problem 1:

• Explanation:
• Step1: Use the consecutive - interior angles theorem
• If lines \(u\) and \(v\) are parallel, then \((x + 63)+(x + 123)=180\) (consecutive - interior angles are supplementary).
• Expand the left - hand side: \(x+63+x + 123=180\), which simplifies to \(2x+186 = 180\).
• Step2: Solve for \(x\)
• Subtract 186 from both sides: \(2x=180 - 186=-6\).
• Divide both sides by 2: \(x=-3\).
• Answer: \(x=-3\), justified by the consecutive - interior angles theorem.

1. Problem 2:

• Explanation:
• Step1: Use the corresponding angles theorem
• If lines \(u\) and \(v\) are parallel, then \(6x + 13=79\) (corresponding angles are equal).
• Step2: Solve for \(x\)
• Subtract 13 from both sides: \(6x=79 - 13 = 66\).
• Divide both sides by 6: \(x = 11\).
• Answer: \(x = 11\), justified by the corresponding angles theorem.

1. Problem 3:

• Explanation:
• Step1: Use the alternate - interior angles theorem
• If lines \(u\) and \(v\) are parallel, then \(7x+17=-1 + 9x\) (alternate - interior angles are equal).
• Step2: Solve for \(x\)
• Subtract \(7x\) from both sides: \(17=-1+9x - 7x\).
• Simplify to \(17=-1 + 2x\).
• Add 1 to both sides: \(18=2x\).
• Divide both sides by 2: \(x = 9\).
• Answer: \(x = 9\), justified by the alternate - interior angles theorem.

1. Problem 4:

• Explanation:
• Step1: Use the corresponding angles theorem
• If lines \(u\) and \(v\) are parallel, then \(13+6x=7x + 6\) (corresponding angles are equal).
• Step2: Solve for \(x\)
• Subtract \(6x\) from both sides: \(13=7x+6 - 6x\).
• Simplify to \(13=x + 6\).
• Subtract 6 from both sides: \(x=7\).
• Answer: \(x = 7\), justified by the corresponding angles theorem.