Question

lines a and b are parallel and lines e and f are parallel. if ( mangle1 = 89^{circ} ), what is ( mangle5 )?

Explanation:

Step1: Find \(m\angle2\)

Since \(\angle1\) and \(\angle2\) are supplementary (they form a linear pair), \(m\angle1 + m\angle2=180^{\circ}\). Given \(m\angle1 = 89^{\circ}\), then \(m\angle2=180 - 89=91^{\circ}\).

Step2: Use parallel - line properties

Because lines \(a\parallel b\) and \(e\parallel f\), \(\angle2\) and \(\angle5\) are corresponding angles. Corresponding angles formed by two pairs of parallel lines are equal. So \(m\angle5 = m\angle2\).

Answer:

\(91\)