Question

given a || b, and c is not parallel to a or b, which statements must be true? select each correct answer. m∠8 = m∠9 m∠7 = m∠10 m∠4 = m∠8 m∠2 = m∠7

Explanation:

Step1: Recall angle - relationships for parallel lines

When \(a\parallel b\) and \(c\) is a transversal, we use the properties of corresponding, alternate - interior, and vertical angles.

Step2: Analyze \(m\angle8 = m\angle9\)

\(\angle8\) and \(\angle9\) are vertical angles. Vertical angles are always equal. So \(m\angle8=m\angle9\) is always true regardless of the parallel - line relationships.

Step3: Analyze \(m\angle7 = m\angle10\)

\(\angle7\) and \(\angle10\) have no special angle relationship based on \(a\parallel b\) and \(c\) not being parallel to \(a\) or \(b\). They are neither corresponding, alternate - interior, vertical, or alternate - exterior angles.

Step4: Analyze \(m\angle4 = m\angle8\)

Since \(a\parallel b\), \(\angle4\) and \(\angle8\) are corresponding angles. Corresponding angles formed by a transversal intersecting two parallel lines are equal. So \(m\angle4 = m\angle8\).

Step5: Analyze \(m\angle2 = m\angle7\)

\(\angle2\) and \(\angle7\) have no special angle relationship based on \(a\parallel b\) and \(c\) not being parallel to \(a\) or \(b\). They are neither corresponding, alternate - interior, vertical, or alternate - exterior angles.

Answer:

\(m\angle8 = m\angle9\), \(m\angle4 = m\angle8\)