Question

line m is parallel to line n when the measure of angle x is. error analysis your friend incorrectly says that line m is parallel to line n when the measure of angle x is 109°. for which measure of angle x is line m parallel to line n? what was your friends likely mistake? (the figure is not to scale.)

Explanation:

Step1: Recall parallel - lines angle property

When two parallel lines are cut by a transversal, corresponding angles are equal, alternate - interior angles are equal, and same - side interior angles are supplementary. In this case, the angle adjacent to the \(71^{\circ}\) angle and angle \(X\) are same - side interior angles.

Step2: Use the supplementary - angle formula

If two angles are supplementary, the sum of their measures is \(180^{\circ}\). Let the measure of angle \(X\) be \(x\). We know that \(x + 71^{\circ}=180^{\circ}\).

Step3: Solve for \(x\)

Subtract \(71^{\circ}\) from both sides of the equation: \(x=180^{\circ}-71^{\circ}=109^{\circ}\). Since your friend is correct when the measure of angle \(X\) is \(109^{\circ}\), the measure of angle \(X\) for which line \(m\) is parallel to line \(n\) is \(109^{\circ}\). There is no error in your friend's statement.

Answer:

\(109\)