Question

given the figure below, find the values of x and z.
(15x + 16)°
(8x + 40)°
z°
x=
z=

Explanation:

Step1: Set up equation using vertical - angle property

Vertical angles are equal. So, $15x + 16=8x + 40$.

Step2: Solve for $x$

Subtract $8x$ from both sides: $15x-8x + 16=8x-8x + 40$, which simplifies to $7x+16 = 40$. Then subtract 16 from both sides: $7x+16 - 16=40 - 16$, giving $7x=24$. Divide both sides by 7: $x=\frac{24}{7}\approx3.43$.

Step3: Find the measure of one of the vertical - angles

Substitute $x = \frac{24}{7}$ into $15x + 16$: $15\times\frac{24}{7}+16=\frac{360}{7}+16=\frac{360 + 112}{7}=\frac{472}{7}\approx67.43$.

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

The angle with measure $(15x + 16)$ and $z$ form a linear - pair, so $(15x + 16)+z = 180$. Substitute $15x + 16=\frac{472}{7}$ into the equation: $\frac{472}{7}+z = 180$. Subtract $\frac{472}{7}$ from both sides: $z=180-\frac{472}{7}=\frac{1260 - 472}{7}=\frac{788}{7}\approx112.57$.

Answer:

$x=\frac{24}{7}$, $z=\frac{788}{7}$