The value of x is 2.
The image shows a diagram of parallel lines cut by a transversal. The parallel lines are labeled M and N, and the transversal is labeled L. Angle X is labeled as an alternate interior angle.
We know that alternate interior angles formed when parallel lines are cut by a transversal are congruent. This means that angle X is congruent to angle 8x - 7.
We are given that the measure of angle 2a + 5 is 8x - 7. Since congruent angles have the same measure, we can set up the following equation:
2a + 5 = 8x - 7
Subtracting 2a from both sides of the equation, we get:
5 = 6x - 7
Adding 7 to both sides of the equation, we get:
12 = 6x
Dividing both sides of the equation by 6, we get:
x = 2
Therefore, the value of x is 2.