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In the given diagram:

- \( AB = AC \) (since the segments have the same markings),
- \( CD = CB \) (also based on the markings).

Given that \( m∠CAD = 25° \), we need to find \( m∠CAB \).

### Analysis:

1. **Triangle \( ABC \) is isosceles**:
   - Since \( AB = AC \), the base angles are equal, so \( m∠CAB = m∠ACB \).

2. **Angle \( ∠CAD \)**:
   - This is given as \( 25° \).

3. **Relation of \( ∠CAB \) and \( ∠CAD \)**:
   - \( ∠CAD \) is an exterior angle to \( ∆ABC \), which means \( m∠CAB = m∠ACD \).
   - Because \( CD = CB \), \( ∆CDB \) is also isosceles, making \( m∠CDB = m∠BCD = 25° \).

Now, in triangle \( ABC \):

- \( m∠ACB = m∠CAB \) (since \( AB = AC \)).
- The angle \( ∠CAB + ∠ACB + ∠BAC = 180° \) (angle sum property of a triangle).

However, because \( ∠CAD \) is an exterior angle, we find:

\[ m∠CAB = 25° \]

Thus, the measure of \( m∠CAB \) is \( 25° \).

Would you like further details or have any questions?

### Relative Questions:

1. How can you use the exterior angle theorem in other triangle problems?
2. Why are the base angles of an isosceles triangle always equal?
3. What is the sum of interior angles in any triangle, and why?
4. How can you determine the other angles in triangle \( ABC \) given \( m∠CAB = 25° \)?
5. What are some properties of isosceles triangles you can use to solve other problems?

### Tip:
Remember, in an isosceles triangle, the angles opposite the equal sides are always equal. This can be a powerful tool when analyzing geometric figures.

Learn how to find the measure of angle m∠CAB given that angle m∠CAD is 25° in an isosceles triangle. Explore the application of the exterior angle theorem and the angle sum property of a triangle. Suitable for high school students studying geometry.

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