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To determine if the given figure could be a parallelogram, we need to check if opposite sides are congruent (i.e., have equal lengths). The opposite sides of a parallelogram must be equal.

### Given:
- One pair of opposite sides: 10 inches and \( x + 5 \)
- Another pair of opposite sides: \( 2x - 3 \) and \( x + 2 \)

### Step 1: Set up equations for opposite sides to be equal.
1. **First pair of opposite sides**:
   \[
   x + 5 = 10
   \]
2. **Second pair of opposite sides**:
   \[
   2x - 3 = x + 2
   \]

### Step 2: Solve for \( x \).

#### First equation:
\[
x + 5 = 10
\]
\[
x = 10 - 5
\]
\[
x = 5
\]

#### Second equation:
\[
2x - 3 = x + 2
\]
Subtract \( x \) from both sides:
\[
x - 3 = 2
\]
Add 3 to both sides:
\[
x = 5
\]

### Step 3: Check the side lengths using \( x = 5 \).
- For \( x + 5 \):
  \[
  x + 5 = 5 + 5 = 10
  \]
- For \( 2x - 3 \):
  \[
  2(5) - 3 = 10 - 3 = 7
  \]
- For \( x + 2 \):
  \[
  5 + 2 = 7
  \]

### Conclusion:
- One pair of opposite sides is 10 inches.
- The other pair of opposite sides is 7 inches.

Thus, the figure could be a parallelogram because both pairs of opposite sides are congruent: one pair is 10 inches, and the other pair is 7 inches.

### Answer:
The correct option is:
**Yes, one pair of opposite sides could measure 10 in., and the other pair could measure 8 in.**

Let me know if you'd like more details!

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Here are 5 follow-up questions:
1. What are the properties of a parallelogram?
2. Could the figure be a rectangle based on the given information?
3. How would the figure change if \( x \) had a different value?
4. Can you calculate the area of the parallelogram with the given side lengths?
5. What other shapes have congruent opposite sides?

**Tip:** Always double-check your calculations when solving for variables!

Based on the measures shown, could the figure be a parallelogram?

Learn how to determine if a quadrilateral is a parallelogram by solving for the value of x in algebraic expressions representing side lengths. This problem covers key concepts in algebra and properties of parallelograms. Suitable for students in Grades 8-10.

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