Question

when the figure below, find the values of x and z.
(7x + 74)°
(6x + 80)°
z°

Explanation:

Step1: Use vertical angles property

Vertical angles are equal. So, \(7x + 74=6x + 80\).

Step2: Solve for \(x\)

Subtract \(6x\) from both sides: \(7x-6x+74 = 6x-6x + 80\), which gives \(x+74=80\). Then subtract \(74\) from both sides: \(x=80 - 74\), so \(x = 6\).

Step3: Find \(z\)

\(z\) and \((7x + 74)\) are supplementary (linear - pair). Substitute \(x = 6\) into \(7x+74\): \(7\times6+74=42 + 74=116\). Then \(z=180-(7x + 74)\). Since \(7x + 74 = 116\), \(z=180 - 116=64\).

Answer:

\(x = 6\) and \(z = 64\)