Question

a pair of parallel lines intersects another pair of parallel lines as shown below. find the value of x.

Explanation:

Step1: Recall angle - property of parallel lines

When two parallel lines are intersected by a transversal, corresponding angles are equal and alternate - interior angles are equal. The angle of 125° and the angle adjacent to \(x\) (on the same side of the transversal) are corresponding angles, so they are equal.

Step2: Use the linear - pair property

The angle adjacent to \(x\) and \(x\) form a linear pair. A linear pair of angles sums up to 180°. Let the angle adjacent to \(x\) be \(y = 125^{\circ}\). Then \(x + y=180^{\circ}\).

Step3: Solve for \(x\)

We have \(x=180 - 125\).
\(x = 55^{\circ}\)

Answer:

\(55\)