Question

lines b and c are parallel. what is the measure of ∠6?
(13x + 9)°
(5x + 9)°
m∠6 = 45°
m∠6 = 54°
m∠6 = 117°
m∠6 = 126°

Explanation:

Step1: Find \(x\)

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: Calculate \(\angle6\)

First, find \(\angle5=(5x + 9)^{\circ}\). Substitute \(x = 9\) into \(\angle5\): \(\angle5=(5\times9+9)^{\circ}=54^{\circ}\).
Since \(\angle6\) and \(\angle5\) are supplementary (\(\angle5+\angle6 = 180^{\circ}\)), then \(\angle6=180^{\circ}-\angle5\).

$$ \angle6=180^{\circ}- 54^{\circ}=126^{\circ} $$

Answer:

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