Question

find the value of the variable and the measure of each labeled angle. (x + 14)° (5x - 38)° x = 13 (type a whole number.) (x + 14)° = □° (type a whole number.)

Explanation:

Step1: Set up the equation

Since the two angles are vertical angles and vertical angles are equal, we set up the equation $x + 14=5x - 38$.

Step2: Solve for x

First, move the x - terms to one side: $38 + 14=5x - x$. So, $52 = 4x$. Then divide both sides by 4: $x=\frac{52}{4}=13$.

Step3: Find the measure of the angle

Substitute $x = 13$ into the expression $x + 14$. We get $(13 + 14)^{\circ}=27^{\circ}$.

Answer:

$x = 13$
$(x + 14)^{\circ}=27^{\circ}$