Question

given the figure below, find the values of x and z. z° (15x - 33)° (9x - 3)° x = z =

Explanation:

Step1: Use vertical - angle property

Vertical angles are equal. So, $15x - 33=9x - 3$.

Step2: Solve for $x$

Subtract $9x$ from both sides: $15x-9x - 33=9x-9x - 3$, which simplifies to $6x-33=-3$. Then add 33 to both sides: $6x-33 + 33=-3 + 33$, giving $6x=30$. Divide both sides by 6: $x = 5$.

Step3: Find the value of one of the angles

Substitute $x = 5$ into $9x - 3$. So, $9\times5-3=45 - 3=42^{\circ}$.

Step4: Find the value of $z$

Since $z$ and the angle $(9x - 3)^{\circ}$ are supplementary (linear - pair, sum to $180^{\circ}$), then $z=180-(9x - 3)$. Substituting $x = 5$, we get $z=180 - 42=138^{\circ}$.

Answer:

$x = 5$
$z = 138$