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, \((13x + 9)+(5x + 9)=180\) (same - side interior angles are supplementary).

$$
LATEXBLOCK0
$$

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

Substitute \(x = 9\) into \(\angle6\)'s adjacent angle \((5x + 9)\)
\(5x+9=5\times9 + 9=45+9 = 54\)
Since \(\angle6\) and \((5x + 9)\) are supplementary (linear pair), \(m\angle6=180-(5x + 9)\)
Substitute \(x = 9\), \(m\angle6=180 - 54=126^{\circ}\)

Answer:

\(m\angle6 = 126^{\circ}\) (the fourth option)