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)° = 27° (type a whole number.)
(5x - 38)° =
(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 $x + 14=5x - 38$.

Step2: Solve for x

Subtract $x$ from both sides: $14 = 4x-38$. Then add 38 to both sides: $14 + 38=4x$, so $52 = 4x$. Divide both sides by 4: $x=\frac{52}{4}=13$.

Step3: Find measure of first - labeled angle

Substitute $x = 13$ into $(x + 14)^{\circ}$, we get $(13 + 14)^{\circ}=27^{\circ}$.

Step4: Find measure of second - labeled angle

Substitute $x = 13$ into $(5x - 38)^{\circ}$, we get $5\times13-38=65 - 38=27^{\circ}$.

Answer:

$x = 13$
$(x + 14)^{\circ}=27^{\circ}$
$(5x - 38)^{\circ}=27^{\circ}$