Question

find the value of each variable and the measure of each angle. (simplify your answers) x = y =

Explanation:

Step1: Use vertical - angle property

Vertical angles are equal. So, we have the equation $4x=(2y - x)$. Also, adjacent angles are supplementary, so $4x+(y + x)=180$.

Step2: Simplify the first equation

From $4x=(2y - x)$, we can rewrite it as $4x+x = 2y$, which gives $5x=2y$, or $y=\frac{5}{2}x$.

Step3: Substitute $y$ into the second equation

Substitute $y=\frac{5}{2}x$ into $4x+(y + x)=180$. We get $4x+(\frac{5}{2}x+x)=180$. Combine like - terms: $4x+\frac{5x + 2x}{2}=180$, $4x+\frac{7x}{2}=180$. Multiply through by 2 to clear the fraction: $8x + 7x=360$, $15x=360$.

Step4: Solve for $x$

Divide both sides of $15x = 360$ by 15, so $x = 24$.

Step5: Solve for $y$

Substitute $x = 24$ into $y=\frac{5}{2}x$. Then $y=\frac{5}{2}\times24=60$.

Answer:

$x = 24$
$y = 60$