Question

find the value of the variable and the measure of each labeled angle. (x + 11)° (5x - 33)° x = (type a whole number.)

Explanation:

Step1: Set the angles equal

Since the two angles are vertical angles and vertical angles are equal, we set up the equation $x + 11=5x - 33$.

Step2: Solve for x

First, subtract $x$ from both sides: $11 = 5x-x - 33$, which simplifies to $11=4x - 33$. Then add 33 to both sides: $11 + 33=4x$, so $44 = 4x$. Divide both sides by 4: $x=\frac{44}{4}=11$.

Step3: Find the measure of the angles

Substitute $x = 11$ into $x + 11$. The measure of each angle is $11+11 = 22^{\circ}$.

Answer:

$x = 11$; Each labeled - angle measures $22^{\circ}$