Question

given the figure below, find the values of x and z. 72° (9x + 9)° z° x =

Explanation:

Step1: Use vertical - angle property

Vertical angles are equal. So, $9x + 9=72$.

Step2: Solve for $x$

Subtract 9 from both sides of the equation: $9x=72 - 9=63$. Then divide both sides by 9: $x=\frac{63}{9}=7$.

Step3: Use linear - pair property

The angle $z$ and the $72^{\circ}$ angle form a linear - pair (sum to $180^{\circ}$). So, $z + 72=180$.

Step4: Solve for $z$

Subtract 72 from both sides: $z=180 - 72 = 108$.

Answer:

$x = 7$, $z = 108$