To solve this problem:

We know that $AOC$ is a straight line. This means that the sum of the angles along the line at point $O$ is $180^\circ$. From the figure:

$80^\circ + 41^\circ + x = 180^\circ$

Simplify the equation:

$121^\circ + x = 180^\circ$

Solve for $x$:

$x = 180^\circ - 121^\circ = 59^\circ$

Final Answer:

$x = 59^\circ$

Would you like more clarification or examples on this? Here are five questions for deeper understanding:

1. Why do angles on a straight line sum to $180^\circ$?
2. Can you solve a similar problem with different angles?
3. What happens if one angle is $x+10$? How do you solve for $x$?
4. How do we apply this concept in polygons?
5. Can this be extended to angles around a point?

Tip: Always check whether a line is straight (sum of $180^\circ$) or a full circle (sum of $360^\circ$) to ensure correct calculations!