Question

ven ( m | n ), find the value of ( x ).
attempt 1 out of 2
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Explanation:

Step1: Use the property of consecutive interior angles

When two parallel lines \(m\parallel n\) are cut by a transversal \(t\), the sum of consecutive - interior angles is \(180^{\circ}\). So, \((7x - 27)+(6x-10)=180\).

Step2: Simplify the left - hand side of the equation

Combine like terms: \(7x+6x-27 - 10=180\), which gives \(13x-37 = 180\).

Step3: Isolate the term with \(x\)

Add \(37\) to both sides of the equation: \(13x-37 + 37=180 + 37\), so \(13x=217\).

Step4: Solve for \(x\)

Divide both sides by \(13\): \(x=\frac{217}{13}=17\).

Answer:

\(17\)