Question

1. find the value of x. then find the measure of each labeled angle. (3x - 10)° (x + 40)° x = 15; both labeled angles are 55°. x = 37.5; the labeled angles are 77.5° and 102.5°. x = 37.5; the labeled angles are 37.5° and 142.5°. x = 25; both labeled angles are 65°.

Explanation:

Step1: Set up equation

Since the two angles are equal (corresponding - angles for parallel - lines), we set up the equation $3x - 10=x + 40$.

Step2: Solve for x

Subtract $x$ from both sides: $3x-x-10=x - x+40$, which simplifies to $2x-10 = 40$. Then add 10 to both sides: $2x-10 + 10=40 + 10$, getting $2x=50$. Divide both sides by 2: $x=\frac{50}{2}=25$.

Step3: Find the measure of the angles

Substitute $x = 25$ into either angle - expression. Using $x + 40$, we have $25+40=65^{\circ}$. Using $3x - 10$, we have $3\times25-10=75 - 10=65^{\circ}$.

Answer:

$x = 25$; both labeled angles are $65^{\circ}$. So the correct option is: $x = 25$; both labeled angles are $65^{\circ}$.