Question

lines b and c are parallel. what is the measure of ∠6? m∠6 = 45° m∠6 = 54° m∠6 = 117° m∠6 = 126°

Explanation:

Step1: Use the property of same - side interior angles

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

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Step2: Find the measure of \(\angle5\)

Substitute \(x = 9\) into \((5x + 9)^{\circ}\), then \(\angle5=(5\times9 + 9)^{\circ}=54^{\circ}\)

Step3: Use the property of supplementary angles

Since \(\angle5+\angle6 = 180^{\circ}\) (linear pair), then \(\angle6=180^{\circ}-\angle5\)
Substitute \(\angle5 = 54^{\circ}\), we get \(\angle6=180^{\circ}-54^{\circ}=126^{\circ}\)

Answer:

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