Question

find the value of x.
7.
8.
9.
10.

Explanation:

7.

Step1: Use the property of parallel lines and transversal (consecutive interior angles)

When two parallel lines are cut by a transversal, consecutive interior angles are supplementary (sum to \(180^{\circ}\)).
Let the angle adjacent to \(110^{\circ}\) be \(y\). Then \(y = 180 - 110=70^{\circ}\) (linear - pair). Since the lines are parallel, \(x=y\) (alternate - interior angles). So \(x = 70\).

8.

Step1: Use the property of parallel lines and transversal (alternate - interior angles)

When two parallel lines are cut by a transversal, alternate - interior angles are equal. The angle of \(70^{\circ}\) and \(x\) are alternate - interior angles. So \(x = 70\).

9.

Step1: Use the property of parallel lines and transversal (corresponding angles)

When two parallel lines are cut by a transversal, corresponding angles are equal. The angle of \(120^{\circ}\) and its corresponding angle (let's call it \(z\)) are equal (\(z = 120^{\circ}\)). Then \(x=180 - z\) (linear - pair). So \(x=180 - 120=60\).

10.

Step1: Use the property of parallel lines and transversal (corresponding angles)

Let the angle adjacent to \(130^{\circ}\) be \(w\). Then \(w = 180 - 130 = 50^{\circ}\) (linear - pair). Since the lines are parallel, \(x = w\) (corresponding angles). So \(x = 50\).

Answer:

1. \(x = 70\)
2. \(x = 70\)
3. \(x = 60\)
4. \(x = 50\)