Question

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

z =

x =

(8x + 45)°

109°

z°

Explanation:

Step1: Find the value of \(x\)

Vertical angles are equal. So, \(8x + 45=109\).
Subtract 45 from both sides: \(8x=109 - 45\), \(8x = 64\).
Divide both sides by 8: \(x=\frac{64}{8}=8\).

Step2: Find the value of \(z\)

Adjacent angles on a straight - line sum to \(180^{\circ}\). So, \(z + 109=180\).
Subtract 109 from both sides: \(z=180 - 109 = 71\).

Answer:

\(x = 8\), \(z = 71\)