Question

note: figure not drawn to scale.
in the figure, line ( q ) is parallel to line ( r ), and both lines are intersected by line ( s ). if ( y = 2x + 8 ), what is the value of ( x )?

Explanation:

Step1: Use the property of parallel lines

Since line \( q\) is parallel to line \( r\) and intersected by line \( s\), \(y + 58=180\) (supplementary angles). So \(y=180 - 58=122\).

Step2: Substitute \(y\) into the equation \(y = 2x+8\)

Substitute \(y = 122\) into \(y = 2x + 8\), we get \(122=2x + 8\).

Step3: Solve for \(x\)

Subtract \(8\) from both sides: \(122-8=2x\), \(114 = 2x\). Then divide both sides by \(2\): \(x=\frac{114}{2}=57\).

Answer:

\(57\)