The triangle in the image has the following angles:

1. $(5x - 17)^\circ$
2. $(7x - 3)^\circ$
3. $56^\circ$

Since the sum of the interior angles of any triangle equals $180^\circ$, we can set up the following equation:

$(5x - 17) + (7x - 3) + 56 = 180$

Let's solve for $x$.The solution to the equation is $x = 12$.

Would you like any additional explanation or have any further questions?

Here are five related questions to expand your understanding:

1. How can we check if the values of the angles are correct once $x$ is known?
2. What happens if the triangle is isosceles? How would that change the problem?
3. How would the formula change if the triangle were an equilateral triangle?
4. Can the sum of angles be different in non-Euclidean geometry?
5. How can you determine if a triangle is acute, obtuse, or right given the angle measures?

Tip: Remember, the sum of the angles in any triangle in Euclidean geometry is always $180^\circ$.