Question

using angle relationships to find a variable
find the value of x that makes l || m.
*
(8x - 77)°
(3x + 38)°

a. what is the angle pair relationship?
b. select the correct equation
c. x =

Explanation:

Step1: Identify angle - pair relationship

When two parallel lines \(l\parallel m\) are cut by a transversal, the given angles \((8x - 77)^{\circ}\) and \((3x+38)^{\circ}\) are alternate - interior angles. Alternate - interior angles are congruent when the lines are parallel.

Step2: Set up the equation

Since the alternate - interior angles are equal, we have the equation \(8x-77 = 3x + 38\).

Step3: Solve the equation for \(x\)

Subtract \(3x\) from both sides:
\(8x-3x-77=3x - 3x+38\)
\(5x-77 = 38\)
Add \(77\) to both sides:
\(5x-77 + 77=38 + 77\)
\(5x=115\)
Divide both sides by \(5\):
\(x=\frac{115}{5}=23\)

Answer:

a. Alternate - interior angles
b. \(8x - 77=3x + 38\)
c. \(23\)