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° (13x + 9)° 2 3 4 5 6 (5x + 9)° 8 a b c

Explanation:

Step1: Use corresponding - angles property

Since lines \(b\) and \(c\) are parallel, the angles \((13x + 9)^{\circ}\) and \((5x+9)^{\circ}\) are corresponding - angles, so \(13x + 9=5x + 9\) is incorrect. They are actually same - side interior angles, and same - side interior angles are supplementary. So, \((13x + 9)+(5x + 9)=180\).

Step2: Solve the equation for \(x\)

First, combine like terms: \(13x+5x+9 + 9=180\), which simplifies to \(18x+18 = 180\). Then subtract 18 from both sides: \(18x=180 - 18=162\). Divide both sides by 18: \(x=\frac{162}{18}=9\).

Step3: Find the measure of \(\angle6\)

The angle \(\angle6\) and \((5x + 9)^{\circ}\) are vertical angles. Substitute \(x = 9\) into \(5x+9\): \(5\times9+9=45 + 9=54\). Since vertical angles are equal, \(m\angle6 = 54^{\circ}\).

Answer:

\(m\angle6 = 54^{\circ}\)