1. The problem involves finding unknown angles or lengths in a geometric figure with a circle and star shape, where angles 60° and 70° are given at point S. 2. To solve problems involving angles in circles and polygons, we use the fact that the sum of angles around a point is 360°, and the sum of angles in a triangle is 180°. 3. Since angles at point S are 60° and 70°, the third angle at S on the baseline is calculated as: $$180^\circ - 60^\circ - 70^\circ = 50^\circ$$ 4. Using this, we can find other angles in triangles formed by points L, M, S, R, and C by applying the triangle angle sum rule. 5. For example, in triangle LSM, if two angles are known, the third can be found by subtracting their sum from 180°. 6. Similarly, use properties of cyclic quadrilaterals and isosceles triangles if applicable, depending on the star shape's symmetry. 7. Without specific lengths or more angle measures, the problem focuses on angle calculations using the given 60° and 70° angles and the geometry rules above. Final answer: The unknown angle at point S on the baseline is $50^\circ$.