Question

name: date: per: math writing given line i parallel to line m and t is the transversal, what is the value of x? explain (in detail) how you solved for x. use specific definitions in your answer.

Explanation:

Step1: Use the property of same - side exterior and interior angles

When two parallel lines \(l\) and \(m\) are cut by a transversal \(t\), the same - side exterior and interior angles are supplementary. So, \(3x+4x + 19=180\).

Step2: Simplify the equation

Combine like terms: \(7x+19 = 180\).

Step3: Solve for \(x\)

Subtract \(19\) from both sides: \(7x=180 - 19\), so \(7x=161\). Then divide both sides by \(7\): \(x=\frac{161}{7}=19\).

Answer:

\(x = 19\)