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To solve for the missing angles in this diagram, we'll need to analyze the relationships between the angles, circles, and triangles in the given figure. Here are some key geometric principles that might be useful for solving this problem:

1. **Circle Properties**: Angles subtended by the same arc in a circle are equal. Also, angles at the center of a circle are twice the angles at the circumference.

2. **Triangle Properties**: In a triangle, the sum of the internal angles is \(180^\circ\).

3. **Cyclic Quadrilaterals**: Opposite angles of a cyclic quadrilateral (a quadrilateral inscribed in a circle) sum up to \(180^\circ\).

4. **Alternate Segment Theorem**: The angle between a tangent and a chord through the point of contact is equal to the angle in the alternate segment.

Let’s address a few angles based on the given information and the labeled angles:

- In the circles where angles are already provided (like \( \angle i = 58^\circ \), \( \angle j = 49^\circ \), and \( \angle h \)), use the property of angles in triangles and circles to find the unknowns.
  
- For example, if \( \angle i \) and \( \angle j \) are angles in a triangle, you can find the third angle \( \angle h \) as:
  \[
  \angle h = 180^\circ - \angle i - \angle j = 180^\circ - 58^\circ - 49^\circ = 73^\circ
  \]

- For angles like \( \angle a \), \( \angle b \), \( \angle c \), or any other labeled angles, consider relationships with angles at the center, angles in the same segment, or angles forming linear pairs.

Would you like me to focus on solving for a specific angle or a particular part of the diagram? Please let me know so I can proceed with a more detailed calculation!

Solve for the missing angle in the provided geometric diagram.

This problem involves solving for the missing angles in a diagram with intersecting circles, triangles, and cyclic quadrilaterals. Key geometry concepts like circle properties, triangle angle sums, and the Alternate Segment Theorem are used. Suitable for Grades 10-12.

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