In any triangle, the sum of the angles is always 180°. We can use this property to set up an equation based on the given angles.

The three angles are:

• $(3x + 2)^\circ$
• $40^\circ$
• $120^\circ$

We know that the sum of the angles in a triangle is 180°, so:

$(3x + 2)^\circ + 40^\circ + 120^\circ = 180^\circ$

Now, solve for $x$:

$3x + 2 + 40 + 120 = 180$

$3x + 162 = 180$

Subtract 162 from both sides:

$3x = 180 - 162$

$3x = 18$

Divide by 3:

$x = \frac{18}{3} = 6$

Thus, the value of $x$ is $\boxed{6}$.

Would you like further details or have any questions?

Here are 5 related questions for further practice:

1. If one angle in a triangle is $(2x + 5)^\circ$, another is $(x - 10)^\circ$, and the third is 70°, what is the value of $x$?
2. The angles of a triangle are in the ratio 2:3:5. Find the angles of the triangle.
3. If two angles in a triangle are 50° and $2x$, find $x$ if the triangle is an isosceles triangle.
4. In a right triangle, one of the acute angles is $(x + 10)^\circ$ and the other is $2x^\circ$. What is $x$?
5. Find the value of $x$ if the exterior angle of a triangle is $(4x - 10)^\circ$ and the two opposite interior angles are 45° and 60°.

Tip: Always remember that the sum of the angles in any triangle is 180°, which is a useful starting point for many problems involving angles.