Question

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

Explanation:

Step1: Use property of parallel lines

When two parallel lines \(m\parallel n\) are cut by a transversal, the corresponding - angles (or alternate - interior/alternate - exterior angles depending on the situation) are equal. Here, we assume the two given angles \((8x - 3)^{\circ}\) and \((6x+27)^{\circ}\) are either corresponding or alternate angles. So we set up the equation \(8x−3 = 6x + 27\).
\[8x−3=6x + 27\]

Step2: Isolate the variable \(x\)

First, subtract \(6x\) from both sides of the equation:
\[8x-6x−3=6x - 6x+27\]
\[2x−3 = 27\]
Then, add 3 to both sides:
\[2x-3 + 3=27 + 3\]
\[2x=30\]
Finally, divide both sides by 2:
\[x=\frac{30}{2}=15\]

Answer:

\(x = 15\)