Question

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

Explanation:

Step1: Use vertical - angle property

Vertical angles are equal. So, $12x + 40=82$.

Step2: Solve for $x$

Subtract 40 from both sides: $12x=82 - 40$, so $12x = 42$. Then divide both sides by 12: $x=\frac{42}{12}=\frac{7}{2}=3.5$.

Step3: Use linear - pair property

The angle $z$ and the $82^{\circ}$ angle form a linear - pair. So $z + 82=180$.

Step4: Solve for $z$

Subtract 82 from both sides: $z=180 - 82 = 98$.

Answer:

$x = 3.5$
$z = 98$