Question

given the figure below, find the values of x and z. 109° (8x + 69)°

Explanation:

Step1: Use vertical - angle property

Vertical angles are equal. So, $5x + 69=109$.

Step2: Solve for $x$

Subtract 69 from both sides of the equation $5x+69 = 109$. We get $5x=109 - 69$, so $5x = 40$. Then divide both sides by 5, $x=\frac{40}{5}=8$.

Step3: Use linear - pair property

The angle $z$ and the 109 - degree angle form a linear pair. So $z + 109=180$.

Step4: Solve for $z$

Subtract 109 from both sides of the equation $z + 109=180$. We get $z=180 - 109 = 71$.

Answer:

$x = 8$
$z = 71$