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 equal to half the difference of the intercepted arcs, or equivalently, the angle between the radii to the points of tangency is twice the angle between the tangents. 3. **Formula:** The angle between the radii is twice the angle between the tangents: $$\text{Angle between radii} = 2 \times \text{Angle between tangents}$$ 4. **Set up the equation:** $$10x = 2 \times 81$$ 5. **Calculate:** $$10x = 162$$ $$x = \frac{162}{10}$$ 6. **Show cancellation:** $$x = \cancel{\frac{162}{\cancel{10}}}16.2$$ 7. **Final answer:** $$x = 16.2$$ This means the value of $x$ is 16.2.