Question

error analysis. your friend incorrectly says that line m is parallel to line n when the measure of angle x is 72°. for which measure of angle x is line m parallel to line n? what was your friends likely mistake?

Explanation:

Step1: Recall parallel - line property

When two lines are parallel, corresponding angles are equal, alternate - interior angles are equal, and same - side interior angles are supplementary. Here, angle \(X\) and the \(108^{\circ}\) angle are same - side interior angles.

Step2: Use the supplementary - angle relationship

If line \(m\) is parallel to line \(n\), then \(X + 108^{\circ}=180^{\circ}\) (since same - side interior angles are supplementary). Solving for \(X\), we get \(X = 180^{\circ}-108^{\circ}\).

Step3: Calculate the value of \(X\)

\(X=72^{\circ}\) is incorrect. The correct value is \(X = 180 - 108=72^{\circ}\) for the non - parallel case. The correct value for parallel lines should be \(X = 72^{\circ}\) based on the supplementary relationship. Your friend likely thought that the \(108^{\circ}\) angle and angle \(X\) were equal (a common error of confusing corresponding or alternate angles with same - side interior angles) instead of supplementary.

Answer:

The measure of angle \(X\) for which line \(m\) is parallel to line \(n\) is \(72^{\circ}\). Your friend's likely mistake was confusing the relationship between the angles and thinking they were equal (like corresponding or alternate angles) instead of supplementary (same - side interior angles).