1. **State the problem:** We are given two intersecting chords in a circle, creating two angles at the intersection point. The angles are labeled as $2x + 41^\circ$ and $12x - 19^\circ$. We need to find the value of $x$. 2. **Recall the property of intersecting chords:** When two chords intersect inside a circle, the opposite angles formed are equal. This means: $$2x + 41 = 12x - 19$$ 3. **Set up the equation and solve for $x$:** $$2x + 41 = 12x - 19$$ Subtract $2x$ from both sides: $$41 = 10x - 19$$ Add $19$ to both sides: $$41 + 19 = 10x$$ $$60 = 10x$$ Divide both sides by 10: $$x = \frac{60}{10} = 6$$ 4. **Conclusion:** The value of $x$ is $6$ degrees. This solution uses the property of intersecting chords in a circle and basic algebraic manipulation to find $x$.