Question

given $m \parallel n$, find the value of x.
(2x - 29)° on line m, (7x + 2)° on line n, with transversal t.

Explanation:

Step1: Use the property of same - side interior angles

When two parallel lines \(m\parallel n\) are cut by a transversal, the sum of same - side interior angles is \(180^{\circ}\). So, \((2x - 29)+(7x + 2)=180\).

Step2: Simplify the left - hand side of the equation

Combine like terms: \(2x+7x-29 + 2=180\), which simplifies to \(9x-27 = 180\).

Step3: Isolate the term with \(x\)

Add \(27\) to both sides of the equation: \(9x-27+27=180 + 27\), getting \(9x=207\).

Step4: Solve for \(x\)

Divide both sides by \(9\): \(x=\frac{207}{9}\).

Answer:

\(x = 23\)