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: $x=\frac{30}{6}=5$.

Step3: Find the measure of one of the angles

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

Step4: Use linear - pair property to find $z$

The angle with measure $z^{\circ}$ and the angle with measure $(9x - 3)^{\circ}$ form a linear - pair, so $z+42 = 180$. Subtract 42 from both sides: $z=180 - 42=138$.

Answer:

$x = 5$
$z = 138$