Question

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

Explanation:

Step1: Use vertical - angle property

Vertical angles are equal. So, \(7x + 85=14x+71\).

Step2: Solve for \(x\)

Subtract \(7x\) from both sides: \(85 = 7x+71\). Then subtract 71 from both sides: \(7x=85 - 71=14\). Divide both sides by 7, we get \(x = 2\).

Step3: Find the value of one of the vertical - angles

Substitute \(x = 2\) into \(7x + 85\), we have \(7\times2+85=14 + 85=99\).

Step4: Find the value of \(z\)

Since \(z\) and the vertical - angle are supplementary (a straight - line is \(180^{\circ}\)), \(z=180-(7x + 85)\). Substitute \(x = 2\) into it, \(z=180 - 99 = 81\).

Answer:

\(x = 2\), \(z = 81\)