1. **Problem statement:** JK is tangent to the circle at point L. The arc LM measures 114° and the angle formed between the tangent JK and chord LM at point L is given as (21x - 24)°. We need to find the value of $x$. 2. **Formula and rule:** The angle between a tangent and a chord is equal to half the measure of the intercepted arc. This means: $$\text{Angle at } L = \frac{1}{2} \times \text{Arc } LM$$ 3. **Set up the equation:** $$21x - 24 = \frac{1}{2} \times 114$$ 4. **Calculate the right side:** $$\frac{1}{2} \times 114 = 57$$ 5. **Solve for $x$:** $$21x - 24 = 57$$ $$21x = 57 + 24$$ $$21x = 81$$ 6. **Divide both sides by 21:** $$x = \frac{81}{21}$$ 7. **Simplify the fraction:** $$x = \frac{\cancel{81}^{3 \times 27}}{\cancel{21}^{3 \times 7}} = \frac{27}{7} \approx 3.857$$ **Final answer:** $$x \approx 3.86$$