1. **Problem statement:** We have a circle with two tangent lines from point K touching the circle at points J and L. The angle between the two tangents at K is 81°. The angle between the radii to points J and L (inside the circle) is given as (10x)°. We need to find the value of $x$. 2. **Key property:** The angle between two tangents from an external point (angle at K) is supplementary to the angle between the radii to the points of tangency. This means: $$\text{Angle at K} + \text{Angle between radii} = 180^\circ$$ 3. **Set up the equation:** $$81^\circ + 10x = 180^\circ$$ 4. **Solve for $x$:** $$10x = 180 - 81$$ $$10x = 99$$ $$x = \frac{99}{10}$$ 5. **Show cancellation:** $$x = \cancel{\frac{99}{\cancel{10}}}9.9$$ 6. **Final answer:** $$x = 9.9$$ This means the value of $x$ is 9.9.