Question

given the figure below, find the values of x and z. (5x - 5)° z° (8x - 44)° x = z =

Explanation:

Step1: Use vertical - angle property

Vertical angles are equal. So, $5x - 5=8x - 44$.

Step2: Solve for $x$

Subtract $5x$ from both sides: $- 5 = 3x-44$. Then add 44 to both sides: $3x=39$, so $x = 13$.

Step3: Find the measure of one of the vertical angles

Substitute $x = 13$ into $5x - 5$. We get $5\times13-5=65 - 5=60$.

Step4: Use the linear - pair property

The angle $z$ and the angle $5x - 5$ are a linear - pair (sum to $180^{\circ}$). So $z=180-(5x - 5)$. Substituting $x = 13$, we have $z = 180 - 60=120$.

Answer:

$x = 13$
$z = 120$