Question

given the figure below, find the values of x and z. (9x + 10)° 109° x = z =

Explanation:

Step1: Use vertical - angle property

Vertical angles are equal. The angle \((9x + 10)^{\circ}\) and \(100^{\circ}\) are vertical angles. So, \(9x+10 = 100\).

Step2: Solve for \(x\)

Subtract 10 from both sides of the equation \(9x+10 = 100\): \(9x=100 - 10=90\). Then divide both sides by 9: \(x=\frac{90}{9}=10\).

Step3: Use linear - pair property

The angle \(z^{\circ}\) and \(100^{\circ}\) form a linear - pair. The sum of angles in a linear - pair is \(180^{\circ}\). So, \(z + 100=180\).

Step4: Solve for \(z\)

Subtract 100 from both sides of the equation \(z + 100=180\): \(z=180 - 100 = 80\).

Answer:

\(x = 10\), \(z = 80\)