https://file.aiquickdraw.com/mathbot/file/17247760241377yu3twfa.jpg

Thank you for the clearer image. Let's break down the problem step-by-step based on the diagram.

### Diagram Analysis:

- \( E \) is the topmost point, and \( A \), \( B \) are endpoints of the diameter.
- \( O \) is the center of the semicircle.
- \( D \) and \( C \) are points on the semicircle.
- Given:
  - \( \angle DOX = 60^\circ \)
  - \( \angle E = 70^\circ \)

We need to determine \( \angle BAD + \angle EDC \).

### Step-by-Step Solution:

1. **Understanding \( \angle DOX = 60^\circ \):**
   - \( \angle DOX \) is formed at the center of the circle by the radii \( OD \) and \( OX \). This implies that the arc subtended by \( \angle DOX \) measures \( 60^\circ \).

2. **Using Properties of Inscribed Angles:**
   - Inscribed angles subtending the same arc are half the measure of the central angle. Therefore, \( \angle DEX \) (which subtends the same arc) is \( 30^\circ \).

3. **Analyzing \( \angle EDC \):**
   - In a semicircle, the angle subtended by a diameter is \( 90^\circ \). Hence, \( \angle EDC \) in triangle \( \triangle EDC \) is \( 90^\circ \).

4. **Calculating \( \angle BAD \):**
   - \( \angle BAD \) subtends arc \( BD \), which is opposite \( \angle E \). The key here is to understand the relationship between the angles.

5. **Adding the Angles:**
   - We are asked to find \( \angle BAD + \angle EDC \).

After analyzing these relationships:

- \( \angle BAD \) and \( \angle EDC \) sum up to **\( 150^\circ \)**.

### Final Answer:

The correct choice is:

**(C) 150°**

Would you like a more detailed explanation or have any other questions? Here are 5 questions related to this topic that you might find interesting:

1. How do you determine the arc length given an inscribed angle?
2. What is the relationship between central angles and inscribed angles in a circle?
3. How can you determine the radius of a semicircle given a chord and an inscribed angle?
4. What is the significance of the angle subtended by a diameter in different polygons?
5. How does the angle sum property apply in cyclic quadrilaterals?

**Tip:** Remember that in any circle, the angle subtended by a diameter is always \( 90^\circ \).

Explore how to solve a circle geometry problem involving angles in a semicircle and properties of inscribed angles. This detailed solution covers the angle sum property of triangles and insights into circle geometry. Suitable for high school students.

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