Question

complete the proof. given: m∠bca = 78°. m∠cfg = 102°. prove: m || n

Explanation:

Step1: Observe angle - sum

We know that \(m\angle BCA = 78^{\circ}\) and \(m\angle CFG=102^{\circ}\), and \(78^{\circ}+ 102^{\circ}=180^{\circ}\).

Step2: Apply parallel - line theorem

If two same - side interior angles formed by two lines \(m\) and \(n\) and a transversal are supplementary (sum to \(180^{\circ}\)), then the two lines are parallel. Here, \(\angle BCA\) and \(\angle CFG\) are same - side interior angles for lines \(m\) and \(n\) with transversal \(AH\).

Answer:

Since \(\angle BCA\) and \(\angle CFG\) are supplementary, we can conclude that \(m\parallel n\).