1. **Problem:** Find the error in the diagram of circle ⊙C and correct it. 2. **Error Analysis:** The error likely involves incorrect angle measures or relationships in the circle diagram. 3. **Correction Methods:** - Method 1: Verify that the inscribed angles subtend the correct arcs and adjust angle measures accordingly. - Method 2: Use the property that the measure of an inscribed angle is half the measure of its intercepted arc to recalculate angles. 4. **Problem:** Name two pairs of congruent angles in the given diagrams. 5. **Solution:** Identify angles with equal measures or corresponding positions in congruent triangles or parallel lines. 6. **Problem:** Find the values of variables $x$ and $y$ given angles $95^\circ$, $80^\circ$, $x^\circ$, and $y^\circ$. 7. **Formula:** Use the fact that the sum of angles around a point or in a triangle is $180^\circ$. 8. **Work:** - For example, if $x$ and $y$ are angles in a triangle with $95^\circ$ and $80^\circ$, then $$x + y + 95 + 80 = 360$$ - Simplify and solve for $x$ and $y$. 9. **Problem:** Find values of $m$ and $k$ given angles $60^\circ$, $m^\circ$, and $2k^\circ$. 10. **Formula:** Use angle sum properties in triangles or polygons. 11. **Work:** - For example, if these angles form a triangle, $$60 + m + 2k = 180$$ - Solve for $m$ and $k$ if additional information is given. 12. **Problem:** Find value of $b$ given angles $4b^\circ$, $54^\circ$, and $130^\circ$. 13. **Formula:** Sum of angles in a triangle is $180^\circ$. 14. **Work:** $$4b + 54 + 130 = 180$$ $$4b + 184 = 180$$ $$4b = \cancel{180} - 184$$ $$4b = -4$$ $$b = \frac{-4}{4} = -1$$ 15. **Interpretation:** Negative angle suggests an error in the problem setup or angle labeling. **Final answers:** - For problem 13: $b = -1$ (check problem context) - For other problems, corrections depend on diagram details.