Question

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

Explanation:

Step1: Identify angle - relationship

Since \(m\parallel n\), the two given angles \((5x + 29)^{\circ}\) and \((8x-16)^{\circ}\) are corresponding angles (or alternate - interior/exterior angles depending on the exact configuration, but they are equal in measure for parallel lines). So we set up the equation \(5x + 29=8x-16\).

Step2: Solve the equation for \(x\)

First, subtract \(5x\) from both sides of the equation:
\(5x+29 - 5x=8x - 16-5x\)
\(29 = 3x-16\).
Then add 16 to both sides:
\(29 + 16=3x-16 + 16\)
\(45 = 3x\).
Finally, divide both sides by 3:
\(x=\frac{45}{3}=15\).

Answer:

\(15\)