https://file.aiquickdraw.com/mathbot/file/1728606269356ovpknyqj.jpg

To solve this problem, let's first understand the diagram and question.

The problem states that \( AC \) is the diameter of circle \( D \), and asks for the sum of \( m \angle A \) and \( m \angle C \). We can apply properties of circles and inscribed angles.

### Key Points:
- \( AC \) is the diameter of the circle.
- In any circle, an angle inscribed in a semicircle (formed by a diameter) is a **right angle** (90°). This is a result of the **inscribed angle theorem**.

### Applying the Theorem:
- Since \( \overline{AC} \) is the diameter, \( \angle ABC \) (an inscribed angle formed with the diameter as one side) must be 90°.
- Therefore, \( \angle A \) and \( \angle C \) are angles in a right triangle where \( \overline{AB} \) and \( \overline{BC} \) are the other two sides.

### Conclusion:
In any right triangle, the two non-right angles must sum to 90°. Hence, 
\[ m\angle A + m\angle C = 90^\circ. \]

Would you like further clarification or more details?

### Related Questions:
1. What is the inscribed angle theorem?
2. Can the sum of angles in a triangle exceed 180°?
3. How do you prove that an angle inscribed in a semicircle is a right angle?
4. What is the relationship between the central and inscribed angles subtended by the same arc?
5. What happens if \( \overline{AC} \) is not the diameter?

### Tip:
In any triangle, the sum of the three interior angles always equals 180°.

If AC is the diameter of circle D, then what is the value of m∠A + m∠C?

Learn how to solve a geometry problem involving a circle where AC is the diameter. By applying the Inscribed Angle Theorem, find the sum of angles A and C in the triangle formed inside the circle. Suitable for students in Grades 8-10.

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