https://file.aiquickdraw.com/mathbot/file/1728693813552ynlfvtge.jpg

In the diagram, we are tasked with finding \(\angle CAE\), and we are given the following information:
- \( BC \parallel DE \),
- \( \angle ABC = 47^\circ \),
- \( \angle CAB = 105^\circ \).

Since lines \(BC\) and \(DE\) are parallel, \(\angle CAE\) and \(\angle ABC\) are alternate interior angles. In parallel lines, alternate interior angles are congruent. Hence, we have:

\[
\angle CAE = \angle ABC = 47^\circ.
\]

Thus, the measure of \(\angle CAE\) is \( 47^\circ \), not 28 degrees as indicated.

Would you like further details on this or any clarifications? 

Here are 5 related questions to explore:
1. What is the significance of alternate interior angles in parallel lines?
2. How can you prove that alternate interior angles are congruent?
3. What other angle relationships exist in parallel line diagrams?
4. How would you calculate unknown angles if one of the parallel lines was tilted?
5. What are corresponding angles, and how do they differ from alternate interior angles?

**Tip:** Always look for parallel lines in a diagram, as they often provide congruent or supplementary angles, simplifying the solution.

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

Learn how to find ∠CAE when given ∠ABC = 47° and ∠CAB = 105°, with lines BC and DE being parallel. Explore key geometry concepts such as alternate interior angles and their congruency in parallel lines. Suitable for students in Grades 7-10.

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