Question

7 find the value of x. show your work.

Explanation:

Step1: Use the property of parallel lines and transversal

When two parallel lines are cut by a transversal, the exterior angle is equal to the sum of the non - adjacent interior angles. Here, \((9x - 12)^{\circ}\) is an exterior angle and \(30^{\circ}\) is one of the non - adjacent interior angles.
So, \(9x-12 = 30\)

Step2: Solve the equation for \(x\)

Add \(12\) to both sides of the equation:
\(9x-12 + 12=30 + 12\)
\(9x=42\)
Divide both sides by \(9\):
\(x=\frac{42}{9}=\frac{14}{3}\approx4.67\)

Answer:

\(x = \frac{14}{3}\)