We are given a triangle with three angles: $56^\circ$, $(2x + 4)^\circ$, and $x^\circ$. The sum of the angles in a triangle is always $180^\circ$. So, we can set up the equation as follows:

$56^\circ + (2x + 4)^\circ + x^\circ = 180^\circ$

Now, let's simplify and solve for $x$:

1. Combine like terms: $56 + 2x + 4 + x = 180$ $60 + 3x = 180$

2. Subtract 60 from both sides: $3x = 120$

3. Divide by 3: $x = 40$

Now that we have $x = 40$, we can find the measures of the three angles:

1. The first angle is given as $56^\circ$.
2. The second angle is $(2x + 4)^\circ = 2(40) + 4 = 80 + 4 = 84^\circ$.
3. The third angle is $x^\circ = 40^\circ$.

Thus, the three angles of the triangle are $56^\circ$, $84^\circ$, and $40^\circ$, which matches option C.

Would you like a more detailed explanation or have any questions?

Here are five related questions for further practice:

1. What is the sum of the interior angles of a polygon with 8 sides?
2. How would the equation change if the first angle was $(3x + 2)^\circ$ instead of $56^\circ$?
3. What are the properties of an equilateral triangle regarding its angles?
4. How do you find the missing angle in a right triangle if you are given two angles?
5. If one angle in a triangle is twice the size of another, how would you set up the equation to solve for the angles?

Tip: Always remember that the sum of the interior angles of a triangle is always $180^\circ$, regardless of the type of triangle.