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 \(\angle6\)

Substitute \(x = 9\) into \((5x + 9)^{\circ}\). First, \(5x+9=5\times9 + 9=45 + 9 = 54\).
\(\angle6\) and \((5x + 9)^{\circ}\) are supplementary (linear pair). So \(m\angle6=180-(5x + 9)\).
Since \(5x + 9 = 54\), then \(m\angle6=180 - 54=126^{\circ}\)

Answer:

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