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, \((13x + 9)^{\circ}\) and \((5x+9)^{\circ}\) are same - side interior angles. The sum of same - side interior angles of two parallel lines is \(180^{\circ}\). So, \((13x + 9)+(5x + 9)=180\).

Step2: Simplify the equation

Combine like terms: \(13x+5x+9 + 9=180\), which gives \(18x+18 = 180\).

Step3: Solve for \(x\)

Subtract 18 from both sides: \(18x=180 - 18=162\). Then divide both sides by 18: \(x=\frac{162}{18}=9\).

Step4: Find the measure of \(\angle6\)

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

Answer:

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