https://file.aiquickdraw.com/mathbot/file/1726329807398ulqp0oyx.jpg

I have opened the image. Let's now solve the given math problems, starting with question 44 and 45.

### **Question 44: Hexagon Problem**

The hexagon provided has labeled angles and side expressions (in terms of \( x \)). Let's solve for \( x \):

Assuming the hexagon is regular:
- A regular hexagon has internal angles of \( 120^\circ \), and all sides are equal.

Given the side expressions in the hexagon diagram, we would typically solve by equating the side lengths or using properties of regular polygons (symmetry, etc.). Since the exact side relationships aren't clear from just this summary, please provide more details if needed, or I can proceed based on regular hexagon assumptions.

### **Question 45: Diagonal Problem in Rectangle ABCD**

Given that the diagonals of a rectangle bisect each other, we can equate the expressions for the segments:

- \( OA = 2x + 4 \)
- \( OD = 3x + 1 \)

Since diagonals bisect each other, \( OA = OD \). So, set the two expressions equal to each other:

\[
2x + 4 = 3x + 1
\]

Solve for \( x \):

\[
2x - 3x = 1 - 4
\]
\[
-x = -3 \implies x = 3
\]

Thus, the value of \( x \) is \( 3 \).

Let me know if you'd like further details or if you'd like help solving question 44 with more context! 

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**Relative Questions:**

1. How do you calculate angles in a regular polygon?
2. What are the properties of diagonals in rectangles?
3. Can a hexagon have different side lengths and still be considered regular?
4. How can we verify if diagonals bisect each other geometrically?
5. What other properties hold for parallelograms that relate to diagonals?

**Tip:** Always check for symmetry in geometric figures, as it often provides useful shortcuts in solving for unknowns.

This page covers how to solve two problems: finding the value of 'x' in a rectangle where diagonals bisect each other and solving for side lengths in a hexagon using algebraic expressions. Suitable for Grades 8-10.

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