Question

what is the value of x in the figure below? (figure shows two parallel horizontal lines cut by a transversal, with one angle labeled 125° and another angle labeled x°)

Explanation:

Step1: Identify supplementary angles

The angle of \(125^\circ\) and its adjacent angle (forming a linear pair) are supplementary, so the adjacent angle is \(180^\circ - 125^\circ\).
\(180 - 125 = 55\)

Step2: Use corresponding angles (parallel lines)

Since the two horizontal lines are parallel and the transversal cuts them, the angle \(x\) and the \(55^\circ\) angle are corresponding angles, so \(x = 55\).

Answer:

\(55\)