Question

geometry problems (partial text due to image):
(22) find the coordinates of the midpoint of a segment with the given endpoints. (make sure to use the midpoint formula)
(23) 45° diagram of angles, find the value of x.
(24) find the values of the variables
(25) find the value of x.

Explanation:

Step1: Identify the angle relationship

The two lines are parallel, and the angle \(60^\circ\) and the angle \((4x - 12)^\circ\) are corresponding angles (or alternate interior angles, depending on the transversal), so they are equal. So we set up the equation \(4x - 12=60\).

Step2: Solve for \(x\)

Add 12 to both sides of the equation: \(4x=60 + 12\), which simplifies to \(4x = 72\). Then divide both sides by 4: \(x=\frac{72}{4}=18\).

Answer:

\(x = 18\)