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In this problem, we are given a triangle with the angles labeled as:

- \( (x + 19)^\circ \),
- \( 41^\circ \),
- \( 105^\circ \).

The sum of the interior angles of any triangle is always \( 180^\circ \). Therefore, we can set up the equation:

\[
(x + 19)^\circ + 41^\circ + 105^\circ = 180^\circ
\]

Now, let's solve this equation step by step.

### Step 1: Combine like terms on the left-hand side.
\[
x + 19 + 41 + 105 = 180
\]

\[
x + 165 = 180
\]

### Step 2: Subtract 165 from both sides to isolate \( x \).
\[
x = 180 - 165
\]

\[
x = 15
\]

So, the value of \( x \) is **15 degrees**.

Would you like more details, or do you have any further questions on this?

Here are some follow-up questions for practice:
1. How do you find the sum of angles in a triangle?
2. What would the equation look like if the angle labeled \( (x + 19)^\circ \) were given as \( (x + 25)^\circ \)?
3. If one of the angles of a triangle is \( 90^\circ \), what type of triangle is it?
4. Can a triangle have two angles that are both greater than \( 90^\circ \)?
5. How would you approach the problem if one angle was unknown, but the two others summed to \( 110^\circ \)?

**Tip**: Always double-check your calculations when solving for an unknown in a geometry problem by ensuring the sum of all angles adds up to 180°.

The measures of the angles of a triangle are shown in the figure below. Solve for x.

Learn how to solve for x in a triangle where the angles are given as (x + 19)°, 41°, and 105°. This problem covers key geometric concepts and the Triangle Angle Sum Theorem. Suitable for students in Grades 6-8.

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