https://file.aiquickdraw.com/mathbot/file/172638215450361f6l4nn.jpg

To solve the given problems, let's break down the diagram and the given angles.

### Part (a): Find \( \angle AED \)

From the diagram:
- \( \angle BAE = 75^\circ \)
- Since \( \angle AED \) is vertically opposite \( \angle BAE \), \( \angle AED = \angle BAE = 75^\circ \)

### Part (b): Find reflex \( \angle BCD \)

- \( \angle ABC = 20^\circ \)
- \( \angle BCD \) and \( \angle ABC \) are adjacent angles along the straight line \( BC \), so the sum of \( \angle BCD \) and \( \angle ABC \) should be \( 180^\circ \).

Calculating \( \angle BCD \):
\[ \angle BCD = 180^\circ - \angle ABC = 180^\circ - 20^\circ = 160^\circ \]

The reflex angle of \( \angle BCD \) is:
\[ 360^\circ - \angle BCD = 360^\circ - 160^\circ = 200^\circ \]

**Results:**
- \( \angle AED = 75^\circ \)
- Reflex \( \angle BCD = 200^\circ \)

Would you like more details or explanations on any part of this solution? Here are some follow-up questions you might consider:
1. Why do vertically opposite angles have the same measure?
2. What is a reflex angle and how is it different from an acute or obtuse angle?
3. How do you determine other angles in a trapezium based on the given angles?
4. What are the properties of a trapezium that are useful in solving geometric problems?
5. How does the sum of the angles in a triangle help in solving problems involving polygons?

**Tip:** Always remember that the sum of angles around a point is \( 360^\circ \), which is useful for finding reflex angles.

In the diagram, ABDE is a trapezium. ∠BAE = 75°, ∠ABC = 20°, and ∠CDE = 40°. Find (a) ∠AED, (b) reflex ∠BCD.

Learn how to find angles in a trapezium, including the vertically opposite angles theorem and reflex angles. This geometry problem involves calculating ∠AED and the reflex ∠BCD, using key geometric formulas and theorems. Suitable for students in Grades 8-10.

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