Question

find the value of the variable and the measure of each labeled angle. (x + 22)° (5x - 42)° x = (type a whole number.)

Explanation:

Step1: Set up equation

Since the two angles are vertical angles and vertical angles are equal, we set up the equation $x + 22=5x - 42$.

Step2: Isolate variable terms

Subtract $x$ from both sides: $22 = 5x-x - 42$, which simplifies to $22=4x - 42$.

Step3: Isolate the $x$ - term further

Add 42 to both sides: $22 + 42=4x$, so $64 = 4x$.

Step4: Solve for $x$

Divide both sides by 4: $x=\frac{64}{4}=16$.

Step5: Find the measure of the angles

Substitute $x = 16$ into $x + 22$: $16+22 = 38$. The other angle $5x-42$ is $5\times16-42=80 - 42=38$.

Answer:

$x = 16$; The measure of each labeled angle is $38^{\circ}$