Question

the lines y and z are parallel. what is the value of x based on the following angles? draw (-x + 138)° (8x - 14)°

Explanation:

Step1: Use the property of alternate - interior angles

Since lines \(Y\) and \(Z\) are parallel, the alternate - interior angles are equal. So, \(-x + 138=8x-14\).

Step2: Solve the equation for \(x\)

Add \(x\) to both sides of the equation:
\(138 = 8x+x-14\), which simplifies to \(138=9x - 14\).
Add \(14\) to both sides: \(138 + 14=9x\), so \(152 = 9x\).
Divide both sides by \(9\): \(x=\frac{152}{9}\approx16.89\).

Answer:

\(x = \frac{152}{9}\)