Question

geometry
transversals (solving)
name the relationship between the angle pairs and then solve for x.
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.

Explanation:

Step1: Identify angle - pair relationship for problem 1

The angles \(118^{\circ}\) and \(x + 118\) are corresponding angles. Corresponding angles are equal when two parallel lines are cut by a transversal. So we set up the equation \(x+118 = 118\).

Step2: Solve the equation for \(x\)

Subtract 118 from both sides of the equation \(x+118=118\).
\(x=118 - 118\)
\(x = 0\)

Since we don't have space to solve all 10 problems, for the general approach for other problems:

1. Identify the angle - pair relationship (alternate - interior, alternate - exterior, corresponding, same - side interior etc.). For example, if two angles are alternate - interior angles and two parallel lines are cut by a transversal, they are equal. If they are same - side interior angles, they are supplementary (sum to \(180^{\circ}\)).
2. Set up an equation based on the angle - pair relationship.
3. Solve the equation for \(x\).

Answer:

For problem 1: \(x = 0\) (The process for other problems is similar as described above)