Question

given the figure below, find the values of x and z. (15x + 16)° (8x + 49)° z° x = z =

Explanation:

Step1: Use vertical - angle property

Vertical angles are equal. So, $15x + 16=8x + 49$.

Step2: Solve for x

Subtract $8x$ from both sides: $15x-8x + 16=8x-8x + 49$, which simplifies to $7x+16 = 49$. Then subtract 16 from both sides: $7x+16 - 16=49 - 16$, getting $7x=33$. Divide both sides by 7: $x=\frac{33}{7}$.

Step3: Find the measure of one of the vertical angles

Substitute $x = \frac{33}{7}$ into $15x + 16$: $15\times\frac{33}{7}+16=\frac{495}{7}+\frac{112}{7}=\frac{495 + 112}{7}=\frac{607}{7}$.

Step4: Use the linear - pair property to find z

The angle with measure $z$ and the angle $15x + 16$ form a linear - pair (sum to 180°). So, $z=180-(15x + 16)$. Substitute $x=\frac{33}{7}$: $z = 180-\frac{607}{7}=\frac{1260}{7}-\frac{607}{7}=\frac{1260 - 607}{7}=\frac{653}{7}$.

Answer:

$x=\frac{33}{7}$, $z=\frac{653}{7}$