Question

find the value of the variable and the measure of each labeled angle. (x + 10)° (4x - 35)° x = (type a whole number).

Explanation:

Step1: Set the two angles equal

Vertical - angles are equal. So, $x + 10=4x-35$.

Step2: Solve for $x$

Subtract $x$ from both sides: $10 = 3x-35$. Then add 35 to both sides: $10 + 35=3x$, so $45 = 3x$. Divide both sides by 3: $x=\frac{45}{3}=15$.

Step3: Find the measure of each angle

Substitute $x = 15$ into $x + 10$. The angle is $15+10 = 25^{\circ}$. Since the vertical - angles are equal, the other labeled angle is also $25^{\circ}$.

Answer:

$x = 15$; The measure of each labeled angle is $25^{\circ}$