X=8.
Following the similarity statement, we know that AC is to DF as BC is to EF. The ratio would be:
24/(x-2) = 20/5
Cross multiply:
24*5 = 20(x-2)
Use the distributive property:
120 = 20x - 40
Add 40 to both sides:
120+40 = 20x - 40 + 40
160 = 20x
Divide both sides by 20:
160/20 = 20x/20
8 = x

Both equations are equivalent, so there are infinitely many solutions.
Answer: 
Step-by-step explanation:
Observe the given figure.
You can identify that the measure of the angle "B" is:

Knowing this, you can conclude that the angle "p" and the angle "m" are Complementary angles, which means that the sum of their measures is 90 degrees. Then, you can write the following equation:
[Equation 1]
You know that:

Then you can substitute it into the [Equation 1] and then solve for
. Therefore, you get:

Answer:
Segment BF = 16
Step-by-step explanation:
The given theorem states that a line parallel to one side of a triangle divides the other two sides proportionately
The given theorem is the Triangle Proportionality Theorem
According to the theorem, given that segment DE is parallel to segment BC, we have;

Therefore;

Which gives;

Similarly, given that EF is parallel to AB, we get;

Therefore;

Which gives;

Therefore, the statement that can be proved using the given theorem is segment BF = 16.