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In the given diagram, you are asked to find the measure of angle \( \angle AEB \).

The diagram shows:
- A right angle at \( \angle CED \).
- \( \angle CEB \) is given as \( 48^\circ \).

Since \( \angle CED \) is a right angle, it measures \( 90^\circ \). The angle \( \angle AEB \) is adjacent to \( \angle CEB \) and forms a right angle together with it.

We can calculate \( \angle AEB \) by subtracting \( \angle CEB \) from \( \angle CED \):

\[ \angle AEB = \angle CED - \angle CEB \]
\[ \angle AEB = 90^\circ - 48^\circ \]
\[ \angle AEB = 42^\circ \]

So, the measure of angle \( \angle AEB \) is \( 42^\circ \).

Would you like any further details or have any questions? Here are some additional questions you might find interesting:

1. How would you find the measure of angle \( \angle CEA \)?
2. What is the sum of the angles around point E?
3. If line segment \( DE \) is extended, what will be the measure of the new angle formed with line segment \( EB \)?
4. How do you verify that \( \angle CED \) is a right angle using the given information?
5. What is the complementary angle of \( \angle CEB \)?

**Tip:** When dealing with angles in geometry, always remember that the sum of angles around a point is \( 360^\circ \) and the sum of angles in a triangle is \( 180^\circ \).

Explore how to find the measure of angle AEB in a geometry problem. Understand the concepts of angles and right angles, with a step-by-step solution provided. Suitable for students in Grades 7-9.

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