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In the given diagram, we are tasked with finding the measure of angle \( \angle CAB \).

### Known information:
- \( AD \perp DC \), meaning that \( \angle ADC = 90^\circ \).
- \( m\angle C = 57^\circ \) (given).
- \( m\angle B = 43^\circ \) (given).

### Approach:
1. **Understanding the structure**: 
   - \( \triangle ABC \) is the triangle of interest.
   - \( AD \) is perpendicular to \( DC \), meaning \( \triangle ADC \) is a right triangle.

2. **Using angle sum property of triangles**: 
   In any triangle, the sum of the interior angles is always \( 180^\circ \). So, in \( \triangle ABC \):
   \[
   m\angle CAB + m\angle B + m\angle C = 180^\circ
   \]
   Substituting the given values:
   \[
   m\angle CAB + 43^\circ + 57^\circ = 180^\circ
   \]
   Simplifying:
   \[
   m\angle CAB + 100^\circ = 180^\circ
   \]
   \[
   m\angle CAB = 180^\circ - 100^\circ = 80^\circ
   \]

Thus, the measure of \( \angle CAB \) is **80°**.

Would you like a detailed breakdown of any of these steps?

### Relative questions:
1. How can the angle sum property be used in different types of triangles?
2. Why is \( AD \perp DC \) relevant in this problem?
3. How do perpendicular lines affect the angles in a triangle?
4. Can you explain how we find unknown angles in any triangle using the given angles?
5. What other properties of triangles could be useful in solving problems like this?

**Tip**: Always check if the sum of angles in any triangle adds up to 180° to verify the correctness of your answer.

In the diagram below, AD ⊥ DC, m∠C = 57° and m∠B = 43°. Find m∠CAB.

Solve for m∠CAB in a triangle where AD ⊥ DC, m∠C = 57°, and m∠B = 43°. Learn how to apply the angle sum property of triangles and basic geometric principles. This problem is suitable for students in Grades 8-10.

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