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The diagram shows a triangle with two given angles: \(\angle ABC = 46^\circ\) and \(\angle ACB = 52^\circ\). We are asked to find the measure of \(\angle CAB\) and \(\angle CAE\).

### Step 1: Find \(\angle CAB\)
In any triangle, the sum of the interior angles is \(180^\circ\). Therefore, to find \(\angle CAB\), we use the following equation:

\[
\angle CAB + \angle ABC + \angle ACB = 180^\circ
\]

Substituting the known values:

\[
\angle CAB + 46^\circ + 52^\circ = 180^\circ
\]

\[
\angle CAB = 180^\circ - 46^\circ - 52^\circ = 82^\circ
\]

Thus, \(\angle CAB = 82^\circ\).

### Step 2: Find \(\angle CAE\)
Since \(AE\) is shown as a straight line, \(\angle CAE\) is a supplementary angle to \(\angle CAB\), meaning:

\[
\angle CAE + \angle CAB = 180^\circ
\]

Substituting the value of \(\angle CAB = 82^\circ\):

\[
\angle CAE = 180^\circ - 82^\circ = 98^\circ
\]

Thus, \(\angle CAE = 98^\circ\).

### Final Answers:
- \(\angle CAB = 82^\circ\)
- \(\angle CAE = 98^\circ\)

Would you like further details on any of the steps or any other questions? Here are five related questions that could expand your understanding:

1. How do we prove that the sum of interior angles in a triangle is always \(180^\circ\)?
2. What are supplementary angles and how are they used in geometry problems?
3. Can you explain how exterior angles of a triangle relate to the interior angles?
4. What is the difference between complementary and supplementary angles?
5. How do straight angles help in finding unknown angles in complex figures?

**Tip:** Always double-check your calculations, especially when working with angle sums and supplementary relationships, as small errors can lead to incorrect conclusions.

What is the measure of ∠CAB and ∠CAE in the diagram below?

In this problem, we solve for the angles ∠CAB and ∠CAE in a triangle using key geometry concepts. Learn how to apply the Triangle Angle Sum Theorem and supplementary angle relationships to solve this question, perfect for students in Grades 7-9.

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