Question

using the following diagram, find the value of x and y. if necessary, state your solution as an improper fraction. (8x - 5)° (10x + 14)° (20y + 1)° x = ______ y = ______ blank 1: blank 2:

Explanation:

Step1: Set up equation for x

Since $(8x - 5)^{\circ}$ and $(10x+14)^{\circ}$ are supplementary (sum to 180°), we have the equation $8x - 5+10x + 14=180$.
Combining like - terms gives $18x+9 = 180$.
Subtract 9 from both sides: $18x=180 - 9=171$.
Divide both sides by 18: $x=\frac{171}{18}=\frac{19}{2}$.

Step2: Set up equation for y

Assume the angle $(20y + 1)^{\circ}$ is supplementary to either of the other two angles. Let's assume it is supplementary to $(8x - 5)^{\circ}$. First, substitute $x=\frac{19}{2}$ into $(8x - 5)$:
$8\times\frac{19}{2}-5=76 - 5 = 71^{\circ}$.
Then, since $(20y + 1)^{\circ}$ and $71^{\circ}$ are supplementary, we have the equation $20y+1+71 = 180$.
Combining like - terms gives $20y+72 = 180$.
Subtract 72 from both sides: $20y=180 - 72 = 108$.
Divide both sides by 20: $y=\frac{108}{20}=\frac{27}{5}$.

Answer:

$x=\frac{19}{2}$
$y=\frac{27}{5}$