The image shows parallel lines cut by a transversal. The expressions represent unknown angle measurements. What is the value of x?

The given two angles, m < 2x + 2° and m < x + 50° are alternate exterior angles.

Alternate exterior angles lie outside the parallel lines, and are on the opposite sides of the transversal. These types of angles have the same measure.

In order to find the measure of both angles, we must first determine the value of x:

2x + 2 = x + 50

Subtract x from both sides:
2x - x + 2 = x - x + 50
x + 2 = 50
Subtract 2 from both sides:
x + 2 - 2 = 50 - 2
x = 48.

Substitute the value of x into the equality statement:

2x + 2° = x + 50°
2(48)° + 2° = 48 + 50°
98° = 98° (True statement, which means that the value of x = 48 is correct).

Therefore, x = 48°

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