https://file.aiquickdraw.com/mathbot/file/17278692654589gg38j60.jpg

In this problem, we are given the following angles in the figure:

- \( \angle FBC = 35^\circ \)
- \( \angle EDC = 34^\circ \)
- \( \angle FAE = 42^\circ \)

We are tasked with finding the measure of \( \angle FEA \).

### Solution:

To find \( \angle FEA \), we need to examine triangle \( AFE \) closely.

- In triangle \( AFE \), we know two angles: \( \angle FAE = 42^\circ \) and \( \angle FBC = 35^\circ \).
- Using the angle sum property of a triangle, which states that the sum of all angles in a triangle is \( 180^\circ \), we can find \( \angle FEA \).

The sum of angles in triangle \( AFE \) is:

\[
\angle FAE + \angle FEA + \angle AFE = 180^\circ
\]

Substitute the known angles:

\[
42^\circ + \angle FEA + 35^\circ = 180^\circ
\]

Simplifying this:

\[
77^\circ + \angle FEA = 180^\circ
\]

\[
\angle FEA = 180^\circ - 77^\circ = 103^\circ
\]

### Answer:
The measure of \( \angle FEA = 103^\circ \).

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Do you need further details or have any other questions? 

Here are some related questions to explore:
1. How do you verify the sum of angles in a triangle?
2. Can this problem be solved using alternate methods like exterior angles?
3. What are the properties of angles in a quadrilateral formed by such triangles?
4. How can this type of problem be applied to coordinate geometry?
5. How do angle bisectors affect the measurements in triangles like this?

**Tip:** Always double-check the sum of angles in a triangle when working through geometry problems to ensure accuracy.

In the given figure, ∠FBC = 35°, ∠EDC = 34°, and ∠FAE = 42°. Find the measure of ∠FEA.

Solve for ∠FEA in triangle AFE given angles ∠FBC = 35°, ∠EDC = 34°, and ∠FAE = 42°. This problem applies the angle sum property of triangles to determine the unknown angle. Suitable for students in Grades 8-10.

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