Question

lines l and m are parallel. what kind of angles are shown in the figure? what does this tell us about their measures? what is the value of x?

Explanation:

Step1: Identify the type of angles

The angles \(134^{\circ}\) and \((16x + 22)^{\circ}\) are alternate - interior angles. Alternate - interior angles are equal when two parallel lines are cut by a transversal.

Step2: Set up the equation

Since the angles are equal, we set up the equation \(16x+22 = 134\).

Step3: Solve the equation for \(x\)

Subtract 22 from both sides of the equation:
\(16x+22-22=134 - 22\)
\(16x=112\)
Divide both sides by 16:
\(x=\frac{112}{16}=7\)

Answer:

\(x = 7\). The angles are alternate - interior angles, so they are equal.