Question

1. what value of x would prove that lines l and m are parallel? 11. what value of x would prove that lines g and r are parallel? 12. what value of y would prove that lines l and m are parallel? (hint: this is the same problem from #7.) 13. determine the missing angle measure and state the angle relationship.

Explanation:

10.

Step1: Identify angle - relationship

If the lines are parallel, the corresponding angles are equal. So, we set up the equation \(7x + 12=9x - 28\).

Step2: Solve the equation for \(x\)

Subtract \(7x\) from both sides: \(12 = 9x-7x - 28\), which simplifies to \(12 = 2x-28\).
Add 28 to both sides: \(12 + 28=2x\), so \(40 = 2x\).
Divide both sides by 2: \(x=\frac{40}{2}=20\).

Step1: Identify angle - relationship

If the lines are parallel, the alternate - interior angles are equal. So, we set up the equation \(7x+8 = 11x - 20\).

Step2: Solve the equation for \(x\)

Subtract \(7x\) from both sides: \(8=11x - 7x-20\), which simplifies to \(8 = 4x-20\).
Add 20 to both sides: \(8 + 20=4x\), so \(28 = 4x\).
Divide both sides by 4: \(x=\frac{28}{4}=7\).

Step1: Identify angle - relationship

If the lines are parallel, the corresponding angles are equal. So, we set up the equation \(7x + 12=9x - 28\) (same as in problem 10).

Step2: Solve the equation for \(x\)

Subtract \(7x\) from both sides: \(12 = 9x-7x - 28\), which simplifies to \(12 = 2x-28\).
Add 28 to both sides: \(12 + 28=2x\), so \(40 = 2x\).
Divide both sides by 2: \(x = 20\). But we want to find \(y\), and if we assume the angle \((y - 70)\) and \((7x + 12)\) are corresponding or some related equal - angle pair (since the hint refers to a previous problem), and if we set \(y-70=7x + 12\). Substitute \(x = 20\) into the equation: \(y-70=7\times20 + 12\).
\(y-70=140 + 12\), \(y-70=152\).
Add 70 to both sides: \(y=152 + 70=222\).

Answer:

\(x = 20\)

11.