Question

given the figure below, find the values of x and z.

Explanation:

Step1: Use vertical - angles property

Vertical angles are equal. So, \(9x - 9=72\).

Step2: Solve for \(x\)

Add 9 to both sides of the equation \(9x - 9=72\): \(9x=72 + 9=81\). Then divide both sides by 9, \(x=\frac{81}{9}=9\).

Step3: Use linear - pair property

The angle \(z\) and the \(72^{\circ}\) angle form a linear - pair. So \(z + 72=180\).

Step4: Solve for \(z\)

Subtract 72 from both sides of the equation \(z + 72=180\), \(z=180 - 72 = 108\).

Answer:

\(x = 9\), \(z = 108\)