Question

15 fill in the blank 2 points find the values of x and y. (18y + 5)° (10x - 61)° (x + 10)° x = type your answer... y = type your answer...

Explanation:

Step1: Set up equation for x

Vertical - angles are equal. So, $10x−61=x + 10$.

Step2: Solve for x

Subtract x from both sides: $10x−x−61=x−x + 10$, which simplifies to $9x−61 = 10$. Then add 61 to both sides: $9x−61 + 61=10 + 61$, getting $9x=71$. Divide both sides by 9: $x=\frac{71}{9}$.

Step3: Set up equation for y

The sum of adjacent - angles forming a straight - line is 180 degrees. Let's assume the angle $(18y + 5)$ and $(10x−61)$ are supplementary. First, substitute $x=\frac{71}{9}$ into $10x−61$: $10\times\frac{71}{9}-61=\frac{710}{9}-\frac{549}{9}=\frac{710 - 549}{9}=\frac{161}{9}$. Then, since $(18y + 5)+\frac{161}{9}=180$. Multiply through by 9 to clear the fraction: $9(18y + 5)+161 = 180\times9$. Expand: $162y+45 + 161 = 1620$. Combine like - terms: $162y+206 = 1620$. Subtract 206 from both sides: $162y=1620 - 206=1414$. Divide by 162: $y=\frac{1414}{162}=\frac{707}{81}$.

Answer:

$x=\frac{71}{9}$
$y=\frac{707}{81}$