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: $m \angle FGH = 115^\circ$.

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.