Question

1. type:__ x =__

Explanation:

Step1: Identify the type of angles

The angles \((13x - 21)^{\circ}\) and \((5x + 75)^{\circ}\) 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 have the equation \(13x-21 = 5x + 75\).

Step3: Solve the equation for \(x\)

Subtract \(5x\) from both sides: \(13x-5x-21=5x - 5x+75\), which simplifies to \(8x-21 = 75\).
Add \(21\) to both sides: \(8x-21 + 21=75 + 21\), so \(8x=96\).
Divide both sides by \(8\): \(x=\frac{96}{8}=12\).

Answer:

Type: Alternate - interior angles; \(x = 12\)