Question

lines l and m are parallel. answer the following questions.
the angles are select alternate interior, which means that they are select congruent.
( x = ) select
the angle marked ( 11x - 28 ) is select degrees.
the angle marked ( 7x - 8 ) is select degrees.

Explanation:

Step1: Set up the equation

Since alternate interior angles are congruent, we have \(7x - 8=11x - 28\).

Step2: Solve for \(x\)

Subtract \(7x\) from both sides: \(-8 = 4x-28\).
Add \(28\) to both sides: \(20 = 4x\).
Divide both sides by \(4\): \(x = 5\).

Step3: Find the measure of \(7x - 8\)

Substitute \(x = 5\) into \(7x - 8\): \(7\times5-8=35 - 8=27\).

Step4: Find the measure of \(11x - 28\)

Substitute \(x = 5\) into \(11x - 28\): \(11\times5-28=55 - 28=27\).

Answer:

\(x = 5\), the angle marked \(7x - 8\) is \(27\) degrees, the angle marked \(11x - 28\) is \(27\) degrees.