Question

given m||n, find the value of x.

Explanation:

Step1: Use property of parallel lines

Since \(m\parallel n\), the given angles \((2x - 29)^{\circ}\) and \((7x+2)^{\circ}\) are supplementary (linear - pair of angles for parallel lines and a transversal), so \((2x - 29)+(7x + 2)=180\).
$$(2x-29)+(7x + 2)=180$$

Step2: Simplify the left - hand side

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

Step3: Isolate the variable term

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

Step4: Solve for x

Divide both sides by 9: \(x=\frac{207}{9}=23\).
$$x = 23$$

Answer:

\(x = 23\)