Question

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

Explanation:

Step1: Use vertical - angle property

Vertical angles are equal. So, \(3x + 50=6x + 20\).

Step2: Solve the equation for \(x\)

Subtract \(3x\) from both sides: \(50 = 3x+20\). Then subtract 20 from both sides: \(30 = 3x\). Divide both sides by 3, we get \(x = 10\).

Step3: Find the value of \(z\)

Since \(z\) and \(3x + 50\) are supplementary (linear - pair of angles, sum to 180°), substitute \(x = 10\) into \(3x + 50\), we have \(3\times10+50=80\). Then \(z=180-(3x + 50)=180 - 80=100\).

Answer:

\(x = 10\), \(z = 100\)