Calculate X in Figure 4.77.

The diameter of the circle is given as $d = 25$.
The radius of the circle is $r = \frac{d}{2} = \frac{25}{2} = 12.5$.
Since the circle is tangent to the bottom horizontal line, the y-coordinate of its center is equal to its radius. So, the center of the circle is $C = (x_c, 12.5)$.
The total height of the block on the left side is $32 + 20 = 52$. So, the top-left corner of the block is at $(0, 52)$ if we set the bottom-left corner of the lower part of the block as $(0,0)$.

The angle given is $113^\circ$, measured from the top horizontal line (at $y=52$) counter-clockwise to the inclined line.
This means the angle between the vertical line (left edge, $x=0$) and the inclined line is $180^\circ - 113^\circ = 67^\circ$.
Therefore, the angle the inclined line makes with the horizontal axis is $90^\circ - 67^\circ = 23^\circ$.
Since the line goes downwards from left to right, its slope is negative.

The inclined line passes through the point $(0, 52)$ and has a slope of $-\tan(23^\circ)$.
The equation of the line is $y - 52 = -\tan(23^\circ) (x - 0)$.
To find the x-intercept, set $y=0$:

Using $\tan(23^\circ) \approx 0.42447$:

So, the inclined line intersects the x-axis at approximately $(122.499, 0)$. Let's call this point $P_x$.

Consider the right-angled triangle formed by the center of the circle $C=(x_c, 12.5)$, the point of tangency on the x-axis $(x_c, 0)$, and the x-intercept of the inclined line $P_x=(122.499, 0)$.
The angle at $P_x$ is $23^\circ$.
The side opposite to this angle is the radius $r = 12.5$.
The side adjacent to this angle is the horizontal distance from $P_x$ to $(x_c, 0)$, which is $122.499 - x_c$.
Using the tangent function:

Rearrange to solve for $x_c$:

From the diagram, the dimension X is the horizontal distance from the left edge ($x=0$) to the vertical line passing through the center of the circle. Therefore, $X = x_c$.

Rounding to two decimal places:

The final answer is 93.05.