Question

given the figure below, find the values of x and z. (7x - 13)° (5x + 17)° z° x = z =

Explanation:

Step1: Use vertical - angle property

Vertical angles are equal. So, $7x - 13=5x + 17$.

Step2: Solve for $x$

Subtract $5x$ from both sides: $7x-5x - 13=5x-5x + 17$, which simplifies to $2x-13 = 17$. Then add 13 to both sides: $2x-13 + 13=17 + 13$, getting $2x=30$. Divide both sides by 2: $x=\frac{30}{2}=15$.

Step3: Find the measure of one of the vertical angles

Substitute $x = 15$ into $7x - 13$, we get $7\times15-13=105 - 13 = 92$.

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

The angle $z$ and the angle $(7x - 13)$ form a linear - pair, so $z+92 = 180$. Subtract 92 from both sides: $z=180 - 92=88$.

Answer:

$x = 15$
$z = 88$