Question

given m||n, find the value of x. (8x - 7)° (x + 16)°

Explanation:

Step1: Use property of parallel lines

When two parallel lines \(m\) and \(n\) are cut by a transversal, the corresponding - angles are equal. Here, \((8x - 7)^{\circ}\) and \((x + 16)^{\circ}\) are corresponding angles. So, we set up the equation \(8x-7=x + 16\).
\[8x-7=x + 16\]

Step2: Isolate the variable \(x\)

Subtract \(x\) from both sides of the equation: \(8x-x-7=x - x+16\), which simplifies to \(7x-7 = 16\).
\[7x-7=16\]

Step3: Add 7 to both sides

\(7x-7 + 7=16 + 7\), resulting in \(7x=23\).
\[7x=23\]

Step4: Solve for \(x\)

Divide both sides by 7: \(x=\frac{23}{7}\approx3.29\).
\[x=\frac{23}{7}\]

Answer:

\(x = \frac{23}{7}\)