Question

1. find the value of x. show your steps.

4.

Explanation:

Step1: Identify angle - relationship

The angles are corresponding angles (assuming the lines are parallel), and corresponding angles are equal.
For the first problem with angles \(128^{\circ}\) and \(2x^{\circ}\), we set up the equation \(2x = 128\).

Step2: Solve for \(x\)

Divide both sides of the equation \(2x = 128\) by 2. So \(x=\frac{128}{2}=64\).
For the second problem with angles \(72^{\circ}\) and \((7x + 24)^{\circ}\), we set up the equation \(7x+24 = 72\).

Step3: Isolate the term with \(x\)

Subtract 24 from both sides of the equation \(7x+24 = 72\). We get \(7x=72 - 24=48\).

Step4: Solve for \(x\)

Divide both sides of the equation \(7x = 48\) by 7. So \(x=\frac{48}{7}\).

Answer:

For the first problem: \(x = 64\)
For the second problem: \(x=\frac{48}{7}\)