1. **Problem Statement:** Find the values of angles $a$ and $b$ in the circle diagrams numbered 7 and 8. 2. **Key Concept:** In a circle, the sum of angles around a point is $360^\circ$. Also, angles on a straight line sum to $180^\circ$. ### For diagram 7: 3. Given angles: $130^\circ$ (one angle), and angles $a$ and $b$ around point $O$. 4. Since angles around point $O$ sum to $360^\circ$, we have: $$a + b + 130^\circ = 360^\circ$$ 5. Rearranging: $$a + b = 360^\circ - 130^\circ = 230^\circ$$ 6. Without additional information, we cannot find unique values for $a$ and $b$, but if $a$ and $b$ are supplementary (on a straight line), then: $$a + b = 180^\circ$$ which contradicts the above. ### For diagram 8: 7. Given angle $130^\circ$ and angles $a$ and $b$. 8. If $a$ and $b$ are angles subtended by the same chord or related by circle theorems, often the sum of opposite angles in cyclic quadrilaterals is $180^\circ$. 9. Assuming $a + b = 130^\circ$ (if they are adjacent to the $130^\circ$ angle), or if $a$ and $b$ are supplementary to $130^\circ$, then: $$a + b = 180^\circ - 130^\circ = 50^\circ$$ 10. Without more details, we cannot determine exact values. **Final answers:** - For diagram 7: $a + b = 230^\circ$ - For diagram 8: $a + b = 50^\circ$ (assuming supplementary angles) If more information is provided, exact values can be found.