The three angles in a triangle have measures of (3x+2)°, 40°, and 120°. What is the value of x?

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.

Solve for x in a triangle where the angles are (3x+2)°, 40°, and 120°. This problem involves understanding the triangle sum theorem and basic algebraic manipulation. Suitable for students in Grades 6-8.

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