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Let's go through the questions one by one and provide the necessary solutions:

### 20. In rectangle ABCD, find \( m \angle BCD \).
- The diagram shows a rectangle, and since \( \angle BCD \) is part of a right triangle formed by the diagonal of the rectangle, \( \angle BCD \) is 45°. This is because diagonals of a rectangle bisect the angles, and each angle formed by the diagonal is 45° in a rectangle.
- **Answer**: \( m \angle BCD = 45^\circ \).

### 21. If \( AB = 7 \), then \( CD = \_\_\_\_\_\_ \).
- In a rectangle, opposite sides are equal. Therefore, if \( AB = 7 \), then \( CD = AB \) because \( AB \parallel CD \).
- **Answer**: \( CD = 7 \).

### 22. If \( AC = 9 \), then \( BD = \_\_\_\_\_\_ \).
- In a rectangle, the diagonals are congruent. Therefore, \( AC = BD \). If \( AC = 9 \), then \( BD = 9 \).
- **Answer**: \( BD = 9 \).

### 23. If \( BX = 8 \), then \( AC = \_\_\_\_\_\_ \).
- The diagram shows that \( BX \) is half of the diagonal, and since diagonals of a rectangle are equal, \( AC = 2 \times BX \).
- **Answer**: \( AC = 16 \).

### 24. In rhombus EFGH, if \( EF = 10 \), then \( EH = \_\_\_\_\_\_ \).
- In a rhombus, all sides are congruent. Therefore, \( EH = EF \). Since \( EF = 10 \), we have:
- **Answer**: \( EH = 10 \).

### 25. Find \( m \angle GOH \).
- In a rhombus, the diagonals bisect each other at right angles. Thus, \( m \angle GOH = 90^\circ \).
- **Answer**: \( m \angle GOH = 90^\circ \).

### 26. If \( OH = 9 \), then \( FH = \_\_\_\_\_\_ \).
- In a rhombus, diagonals bisect each other. Therefore, \( OH \) is half of the full diagonal \( FH \). So, \( FH = 2 \times OH = 2 \times 9 = 18 \).
- **Answer**: \( FH = 18 \).

### 27. If \( m \angle FEH = 65^\circ \), then \( m \angle FGH = \_\_\_\_\_\_ \).
- In a rhombus, opposite angles are equal, and the sum of adjacent angles is 180°. Since \( \angle FEH + \angle FGH = 180^\circ \), we can calculate \( m \angle FGH = 180^\circ - 65^\circ = 115^\circ \).
- **Answer**: \( m \angle FGH = 115^\circ \).

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Would you like further details or clarifications on any of these? Here are five related questions to explore further:

1. What are the properties of a rhombus that distinguish it from a square?
2. How do you calculate the length of the diagonal in a rectangle given the side lengths?
3. Why are the diagonals of a rectangle always congruent?
4. How do the diagonals of a rhombus affect its symmetry and angles?
5. Can you explain why opposite angles in a rhombus are always equal?

**Tip**: In any quadrilateral with equal diagonals, such as rectangles, the properties of symmetry help simplify many angle and length calculations.

In rectangle ABCD, find m∠BCD. If AB = 7, then CD = ___. If AC = 9, then BD = ___. If BX = 8, then AC = ___. In rhombus EFGH, if EF = 10, then EH = ___. Find m∠GOH. If OH = 9, then FH = ___. If m∠FEH = 65, then m∠FGH = ___.

Solve problems involving angles and sides in rectangles and rhombuses. Learn how to find unknown angles and side lengths using properties like diagonal congruence, angle bisectors, and sum of angles in polygons. Suitable for students in Grades 7-9.

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