Question

find the value of the variable and the measure of each labeled angle.
(x + 16)° (5x - 24)°
x = 10 (type a whole number.)
(x + 16)° = □° (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 $x + 16=5x - 24$.

Step2: Solve for x

Subtract $x$ from both sides: $16 = 4x-24$. Then add 24 to both sides: $40 = 4x$. Divide both sides by 4, so $x = 10$.

Step3: Find the measure of the angle

Substitute $x = 10$ into the expression $x + 16$. We get $10+16=26$.

Answer:

$x = 10$
$(x + 16)^{\circ}=26^{\circ}$