Question

find the value of the variable and the measure of each labeled angle.
(type a whole number.)

Explanation:

Step1: Set up equation using vertical - angle property

Vertical angles are equal. So, $4x - 30=x + 15$.

Step2: Solve for $x$

Subtract $x$ from both sides: $4x - x-30=x - x + 15$, which simplifies to $3x-30 = 15$. Then add 30 to both sides: $3x-30 + 30=15 + 30$, giving $3x=45$. Divide both sides by 3: $\frac{3x}{3}=\frac{45}{3}$, so $x = 15$.

Step3: Find the measure of the angle

Substitute $x = 15$ into either $4x - 30$ or $x + 15$. Using $x + 15$, we get $15+15=30$.

Answer:

$x = 15$, and the measure of the labeled angle is $30$