Question

given the figure below, find the values of x and z.
(11x - 59)°
(7x - 13)°
z°
x=
z=

Explanation:

Step1: Set up equation using vertical - angle property

Vertical angles are equal. So, $11x - 59=7x - 13$.

Step2: Solve for x

Subtract $7x$ from both sides: $11x-7x - 59=7x-7x - 13$, which simplifies to $4x-59=-13$. Then add 59 to both sides: $4x-59 + 59=-13 + 59$, giving $4x = 46$. Divide both sides by 4: $x=\frac{46}{4}=\frac{23}{2}=11.5$.

Step3: Find the measure of one of the vertical angles

Substitute $x = 11.5$ into $7x-13$. So, $7\times11.5-13=80.5 - 13=67.5$.

Step4: Find z

Since $z$ and the angle $7x - 13$ are supplementary (linear - pair, sum to 180°), then $z=180-(7x - 13)$. Substituting $x = 11.5$, we get $z = 180 - 67.5=112.5$.

Answer:

$x = 11.5$
$z = 112.5$