We are given the equation of the first line, $y = 2x + X$, and the point $(5, 5)$ that the second line passes through.
To find the intersection point of these two lines, we need to find the coordinates $(x, y)$ that satisfy both equations.
The first line has a slope of 2, so the slope of the perpendicular line would be the negative reciprocal, which is $-\frac{1}{2}$.
Using the point-slope form of a line, we can write the equation of the perpendicular line as:
$y - 5 = -\frac{1}{2}(x - 5)$
Simplifying this equation, we get:
$y - 5 = -\frac{1}{2}x + \frac{5}{2}$
$y = -\frac{1}{2}x + \frac{15}{2}$
Now, we can set the two equations equal to each other to find the intersection point:
$2x + X = -\frac{1}{2}x + \frac{15}{2}$
Multiplying both sides of the equation by 2 to eliminate the fraction, we get:
$4x + 2X = -x + 15$
Adding $x$ to both sides of the equation, we find:
$5x + 2X = 15$
Now, we can solve this equation for $x$:
$5x = 15 - 2X$
Dividing both sides of the equation by 5, we get:
$x = \frac{15 - 2X}{5}$
Given that the intersection point is (1, 7), we can substitute these coordinates into the equation:
$x = 1$ and $y = 7$
Substituting these values into the equation $x = \frac{15 - 2X}{5}$, we get:
$1 = \frac{15 - 2X}{5}$
Multiplying both sides of the equation by 5 to eliminate the fraction, we find:
$5 = 15 - 2X$
Subtracting 15 from both sides of the equation, we get:
$-10 = -2X$
Dividing both sides of the equation by -2, we find:
$X = 5$
The value of X is 5.
The answer is: 5
Below is a math problem. Provide a detailed, step-by-step solution.

### Problem:
What is the intersection point of the line $y = 2x + X and the line perpendicular to it that passes through the point $(5, 5)$?
If we know the answer to the above question is (1,7), what is the value of unknown variable X?

### Answer:
