Question

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

x=
z=

Explanation:

Step1: Use vertical angles property

Vertical angles are equal. So, \(7x + 60=11x + 36\).

Step2: Solve for \(x\)

Subtract \(7x\) from both sides: \(60 = 4x+36\).
Subtract \(36\) from both sides: \(24 = 4x\).
Divide both sides by \(4\): \(x = 6\).

Step3: Find \(z\)

\(z\) and \((7x + 60)\) are supplementary (linear - pair). So \(z+(7x + 60)=180\).
Substitute \(x = 6\) into \(7x+60\): \(7\times6 + 60=42 + 60=102\).
Then \(z=180-(7x + 60)=180 - 102=78\).

Answer:

\(x = 6\), \(z = 78\)