https://file.aiquickdraw.com/mathbot/file/1729111710465lkf73tx0.jpg

To solve this problem, let's analyze the given information and the diagram:

### Given:
- \( BC \parallel DE \) (line BC is parallel to line DE)
- \( \angle ABC = 47^\circ \)
- \( \angle CAB = 105^\circ \)

### To Find:
- \( \angle CAE \)

### Solution:
1. **Using the Parallel Line Property**: Since \( BC \parallel DE \) and \( AC \) acts as a transversal, the angles on either side of the transversal are corresponding. Thus:
   - \( \angle ABC \) corresponds to \( \angle CAE \).

2. **Corresponding Angles**:
   - \( \angle CAE = \angle ABC = 47^\circ \).

Thus, \( \angle CAE = 47^\circ \).

Would you like a deeper explanation or have any questions? Here are some related questions for practice:

1. If \( \angle DAE = 105^\circ \), what is \( \angle DAB \)?
2. What would be the measure of \( \angle ACD \) given \( \angle CAB \) and \( BC \parallel DE \)?
3. How do corresponding angles relate when two lines are parallel?
4. If \( \angle BCA \) is \( 28^\circ \), how does it affect \( \angle BAE \)?
5. What is the sum of the interior angles of triangle ABC?

**Tip**: Remember, corresponding angles are equal when a transversal intersects two parallel lines!

In the below diagram, line BC is parallel to DE, and given that ∠ABC = 47° and ∠CAB = 105°, find ∠CAE.

Learn how to find ∠CAE when two lines are parallel. Given that ∠ABC = 47° and ∠CAB = 105°, we use the corresponding angles theorem to solve this problem. Suitable for students in Grades 8-10.

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