Question

find the value of the variable and the measure of each labeled angle. (x + 16)° (5x - 24)° x = (type a whole number.)

Explanation:

Step1: Set up the equation

Vertical - angles are equal. So, $x + 16=5x - 24$.

Step2: Isolate the variable terms

Subtract $x$ from both sides: $16 = 5x-x - 24$, which simplifies to $16=4x - 24$.

Step3: Isolate the $x$ - term

Add 24 to both sides: $16 + 24=4x$, so $40 = 4x$.

Step4: Solve for $x$

Divide both sides by 4: $x=\frac{40}{4}=10$.

Step5: Find the measure of the angles

Substitute $x = 10$ into either expression for the angle. Using $x + 16$, we get $10+16 = 26^{\circ}$.

Answer:

$x = 10$; The measure of each labeled angle is $26^{\circ}$