Question

given ( m parallel n ), find the value of ( x ).

Explanation:

Step1: Identify angle relationship

Since \( m \parallel n \) and \( t \) is a transversal, the two angles \((x - 17)^\circ\) and \((3x + 1)^\circ\) are same - side interior angles. Same - side interior angles are supplementary, so their sum is \( 180^\circ \).
We can write the equation: \((x - 17)+(3x + 1)=180\)

Step2: Simplify the left - hand side of the equation

Combine like terms: \(x-17 + 3x+1=180\)
\(x+3x-17 + 1=180\)
\(4x-16 = 180\)

Step3: Solve for \(x\)

Add 16 to both sides of the equation: \(4x-16 + 16=180 + 16\)
\(4x=196\)
Divide both sides by 4: \(x=\frac{196}{4}=49\)

Answer:

\(x = 49\)