This image shows a triangle with angles labeled in terms of $x$. We need to find the value of $x$.

To solve this, we use the fact that the sum of all angles in a triangle is always 180°. The two angles provided in the image are $(3x - 33)^\circ$ and $(x + 11)^\circ$. The third angle, which is marked as $x^\circ$, can be represented as $x$.

So, the equation based on the sum of the angles is:

$(3x - 33) + (x + 11) + x = 180$

Let’s solve for $x$:

$3x - 33 + x + 11 + x = 180$

Simplify the terms:

$5x - 22 = 180$

Add 22 to both sides:

$5x = 202$

Now divide both sides by 5:

$x = \frac{202}{5} = 40.4$

So, $x = 40.4^\circ$.

Would you like further explanation or have other questions?

Here are 5 related questions for you to consider:

1. What is the definition of an angle in a triangle?
2. How do you check if the angles in a triangle add up to 180°?
3. What happens if the sum of the angles is not equal to 180° in a triangle?
4. How do you solve equations with variables in multiple terms?
5. How do you apply angle relationships to real-life situations?

Tip: When solving angle problems, always double-check your angle sum, especially in polygons like triangles.