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°.