Question

if ( mangle1 = 7x - 36 ) and ( mangle2 = 5x + 12 ), for which value of ( x ) would ( pparallel q )?

Explanation:

Step1: Use the property of parallel lines

When \(p\parallel q\), \(\angle1\) and \(\angle2\) are supplementary. So \(m\angle1 + m\angle2=180^{\circ}\).

Step2: Substitute the given expressions

Substitute \(m\angle1 = 7x - 36\) and \(m\angle2 = 5x + 12\) into the equation \(m\angle1 + m\angle2 = 180\).
We get \((7x - 36)+(5x + 12)=180\).

Step3: Simplify the equation

Combine like - terms: \(7x+5x-36 + 12=180\), which simplifies to \(12x-24 = 180\).

Step4: Solve for \(x\)

Add \(24\) to both sides: \(12x=180 + 24\), so \(12x=204\).
Divide both sides by \(12\): \(x=\frac{204}{12}=17\).

Answer:

1. \(17\)