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transversal problems with equations (level 1
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given ( m | n ), find the value of ( x ).
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attempt 1 out of 3
( x = )
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Explanation:

Step1: Use the property of parallel lines

When two parallel lines \(m\parallel n\) are cut by a transversal, the sum of consecutive - interior angles is \(180^{\circ}\). So, \((6x - 7)+(3x + 16)=180\).

Step2: Simplify the left - hand side of the equation

Combine like terms: \(6x+3x-7 + 16=180\), which simplifies to \(9x+9 = 180\).

Step3: Isolate the variable term

Subtract 9 from both sides of the equation: \(9x+9-9=180 - 9\), so \(9x=171\).

Step4: Solve for \(x\)

Divide both sides by 9: \(x=\frac{171}{9}\).

Answer:

\(x = 19\)