Question

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

Step1: Use the property of same - side interior angles

When two parallel lines \(m\parallel n\) are cut by a transversal \(t\), the sum of same - side interior angles is \(180^{\circ}\). So, \((x + 5)+(3x+7)=180\).

Step2: Simplify the equation

Combine like terms: \(x+3x+5 + 7=180\), which gives \(4x+12 = 180\).

Step3: Solve for \(x\)

Subtract \(12\) from both sides: \(4x=180 - 12=168\). Then divide both sides by \(4\): \(x=\frac{168}{4}=42\).

Answer:

\(42\)