Question

in the figure below, g || h. find the values of z and x.

Explanation:

Step1: Identify angle - relationship

Since \(g\parallel h\), the \(84^{\circ}\) angle and \((3x - 12)^{\circ}\) are corresponding angles and are equal.

$$3x-12 = 84$$

Step2: Solve for \(x\)

Add 12 to both sides of the equation:

$$3x=84 + 12$$

$$3x=96$$

Divide both sides by 3:

$$x=\frac{96}{3}=32$$

The angle \(z\) and the \(84^{\circ}\) angle are vertical - angles. Vertical angles are equal. So \(z = 84\).

Answer:

\(x = 32\), \(z = 84\)