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!