1. **State the problem:** We need to determine the values of the angles $a^\circ$, $b^\circ$, and $c^\circ$ shown in the graph around the origin in the Cartesian coordinate system. 2. **Understand the setup:** The angles $a$, $b$, and $c$ are formed between the coordinate axes and the colored sections. Since these angles are centered at the origin and arranged around the coordinate axes, their sum should be $360^\circ$ because they cover the full circle around the origin. 3. **Use the angle sum rule:** The sum of angles around a point is $$a + b + c = 360^\circ$$ 4. **Additional information:** Typically, if the angles are formed by coordinate axes and the colored sections, some of these angles might be complementary or supplementary depending on the exact figure. However, since the problem does not provide explicit numeric values or relationships, we assume the angles are parts of the full circle. 5. **Conclusion:** Without additional numeric data or relationships, the best we can say is $$a + b + c = 360^\circ$$ If you provide numeric values or relationships between $a$, $b$, and $c$, we can solve for their exact values.