Question

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

Explanation:

Step1: Use vertical - angle property

Vertical angles are equal. So, $9x + 54=10x + 51$.

Step2: Solve for $x$

Subtract $9x$ from both sides: $54=x + 51$. Then subtract 51 from both sides, we get $x = 3$.

Step3: Find the measure of one of the angles

Substitute $x = 3$ into $9x+54$. So, $9\times3 + 54=27+54 = 81$.

Step4: Use linear - pair property

The angle of measure $z$ and the angle of measure $9x + 54$ (which is 81) are a linear - pair. So, $z+81 = 180$.

Step5: Solve for $z$

Subtract 81 from both sides: $z=180 - 81=99$.

Answer:

$x = 3$
$z = 99$