Question

m∠6 = 45° m∠6 = 54° m∠6 = 117° m∠6 = 126°

Explanation:

Step1: Use the property of same - side exterior angles

Since lines \(b\) and \(c\) are parallel and \(a\) is a transversal, \((13x + 9)^{\circ}+(5x + 9)^{\circ}=180^{\circ}\) (same - side exterior angles are supplementary).

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Step2: Find the measure of \(\angle6\)

Substitute \(x = 9\) into the expression for \(\angle6\). \(\angle6=(13x + 9)^{\circ}\) (corresponding angles: \(\angle2\) and \(\angle6\) are corresponding angles when \(b\parallel c\) and \(a\) is a transversal).
When \(x = 9\), \(13x+9=13\times9 + 9=117 + 9=126\)

Answer:

\(m\angle6 = 126^{\circ}\)