https://file.aiquickdraw.com/mathbot/file/1726053189504ptz3kcex.jpg

Let's analyze and solve the problem in the image:

### The image provides:
- Several angles in a polygon-like structure.
- Angles labeled \( A \), \( B \), \( C \), \( D \), and \( E \) are to be determined.

### Using some basic angle properties:
1. **Linear pair of angles**: If two angles form a straight line, they add up to 180°.
2. **Sum of external angles** of any polygon equals 360°.
3. **Interior angle + exterior angle = 180°**.

### Let's calculate each angle step by step:

1. **Angle \( \angle A \)**:
   \[ \text{Given: External angle adjacent to \( A \) is } 125^\circ. \]
   \[ \angle A = 180^\circ - 125^\circ = 55^\circ \]

2. **Angle \( \angle B \)**:
   \[ \text{Given: Internal angle adjacent to \( B \) is } 60^\circ. \]
   \[ \angle B = 180^\circ - 60^\circ = 120^\circ \]

3. **Angle \( \angle C \)**:
   \[ \text{Given: Internal angle adjacent to \( C \) is } 70^\circ. \]
   \[ \angle C = 180^\circ - 70^\circ = 110^\circ \]

4. **Angle \( \angle D \)**:
   \[ \text{Given: Internal angle adjacent to \( D \) is } 65^\circ. \]
   \[ \angle D = 180^\circ - 65^\circ = 115^\circ \]

5. **Angle \( \angle E \)**:
   \[ \text{Given: Internal angle adjacent to \( E \) is } 40^\circ. \]
   \[ \angle E = 180^\circ - 40^\circ = 140^\circ \]

### Final answers:
1. \( \angle A = 55^\circ \)
2. \( \angle B = 120^\circ \)
3. \( \angle C = 110^\circ \)
4. \( \angle D = 115^\circ \)
5. \( \angle E = 140^\circ \)

Do you have any questions or would you like further details? 

Here are 5 related questions for practice:
1. How do you find the exterior angle of a polygon?
2. What is the sum of the interior angles of a polygon with \( n \) sides?
3. How can you verify if a set of angles forms a polygon?
4. Can an interior angle be larger than 180°?
5. How do you calculate angles in a regular polygon?

**Tip:** When solving problems involving linear pairs, always remember that the sum of angles on a straight line is 180°.

What is the measure of angles A, B, C, D, and E in the given diagram?

Learn how to determine the angles A, B, C, D, and E in a geometric diagram by applying the linear pair theorem. This solution explains how to find each angle step by step by understanding the relationship between internal and external angles.

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