Question

in the diagram below, line m intersects line n.
what is the measure of \\(\angle x\\)?

Explanation:

Step1: Identify vertical angles

Vertical angles are equal. The angle opposite to the \(45^\circ\) angle (formed by intersecting lines \(m\) and \(n\)) is also \(45^\circ\).

Step2: Calculate \( \angle x \)

The \(45^\circ\) angle is composed of \( \angle x \) and the \(17^\circ\) angle. So, we subtract \(17^\circ\) from \(45^\circ\) to find \( \angle x \).

$$ x = 45^\circ - 17^\circ = 28^\circ $$

Answer:

\(28\)