Question

using parallel lines to find a variable
given the lines are parallel, solve for the missing variable
a. what is the angle pair relationship?
b. select the correct equation
c. y =

Explanation:

Step1: Determine the angle - pair relationship

When two parallel lines are cut by a transversal, alternate - interior angles are equal. Here, the angles \(40^{\circ}\) and \((5y - 10)^{\circ}\) are alternate - interior angles.

Step2: Set up the equation

Since alternate - interior angles are equal, we set \(5y-10 = 40\).

Step3: Solve the equation for \(y\)

Add \(10\) to both sides of the equation:
\(5y-10 + 10=40 + 10\)
\(5y=50\)
Divide both sides by \(5\):
\(y=\frac{50}{5}=10\)

Answer:

a. Alternate - interior angles
b. \(5y - 10=40\)
c. \(y = 10\)