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### Questions Extracted:
1. **What is the measure of each interior angle of a regular pentagon?**
2. **In a parallelogram, adjacent angles are equal. Find the measure of all angles of this parallelogram. What is the name of this special parallelogram?**
3. **A line graph which is a whole unbroken line is called a ________ graph.**
4. **The standard form for \(0.000064\) is _______.**
5. **Is it possible to have a quadrilateral in which all the angles are obtuse? Explain your answer.**
6. **The area of a rhombus is \(120 \, \text{cm}^2\). If its one diagonal is \(20 \, \text{cm}\), find the other diagonal.**
7. **What will be the side of a cube whose surface area is \(2400 \, \text{cm}^2\)?**

### Answers:

1. **Measure of each interior angle of a regular pentagon:**
   The formula for the measure of an interior angle of a regular polygon is:
   \[
   \text{Interior Angle} = \frac{(n-2) \times 180^\circ}{n}
   \]
   For a pentagon (\(n = 5\)):
   \[
   \text{Interior Angle} = \frac{(5-2) \times 180^\circ}{5} = \frac{3 \times 180^\circ}{5} = 108^\circ
   \]
   **Answer: 108°**

2. **Angles of a parallelogram with equal adjacent angles:**
   In a parallelogram, opposite angles are equal, and adjacent angles are supplementary. If adjacent angles are equal, both angles must be \(90^\circ\), making the parallelogram a rectangle.
   **Answer: All angles are \(90^\circ\), and the parallelogram is a rectangle.**

3. **A line graph which is a whole unbroken line:**
   **Answer: A continuous graph.**

4. **Standard form of \(0.000064\):**
   Standard form is also known as scientific notation. We move the decimal point 5 places to the right:
   \[
   0.000064 = 6.4 \times 10^{-5}
   \]
   **Answer: \(6.4 \times 10^{-5}\).**

5. **Is it possible to have a quadrilateral with all obtuse angles?**
   No, it is not possible. The sum of the interior angles of any quadrilateral is \(360^\circ\). An obtuse angle is greater than \(90^\circ\). If all four angles were obtuse, their sum would exceed \(360^\circ\), which is not possible.
   **Answer: No, it is not possible.**

6. **Find the other diagonal of a rhombus:**
   The area of a rhombus is given by:
   \[
   \text{Area} = \frac{1}{2} \times d_1 \times d_2
   \]
   where \(d_1\) and \(d_2\) are the diagonals. Given:
   \[
   \text{Area} = 120 \, \text{cm}^2, \quad d_1 = 20 \, \text{cm}
   \]
   Substituting into the formula:
   \[
   120 = \frac{1}{2} \times 20 \times d_2
   \]
   Solving for \(d_2\):
   \[
   d_2 = \frac{120 \times 2}{20} = 12 \, \text{cm}
   \]
   **Answer: The other diagonal is \(12 \, \text{cm}\).**

7. **Find the side of a cube with a surface area of \(2400 \, \text{cm}^2\):**
   The surface area \(S\) of a cube is given by:
   \[
   S = 6s^2
   \]
   where \(s\) is the side length of the cube. Given:
   \[
   2400 = 6s^2
   \]
   Solving for \(s^2\):
   \[
   s^2 = \frac{2400}{6} = 400
   \]
   Taking the square root:
   \[
   s = \sqrt{400} = 20 \, \text{cm}
   \]
   **Answer: The side length is \(20 \, \text{cm}\).**

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Let me know if you want more details or explanations on any of these answers. Here are 5 related questions to consider:

1. What is the sum of interior angles of a regular hexagon?
2. How do you calculate the exterior angle of any regular polygon?
3. What are the properties of a rhombus in relation to its diagonals?
4. Can a quadrilateral have exactly two obtuse angles? Why or why not?
5. How do you convert a number like \(8.5 \times 10^3\) into standard form?

**Tip:** Always remember that the sum of interior angles in any polygon is given by \((n-2) \times 180^\circ\), where \(n\) is the number of sides.

What is the measure of each interior angle of a regular pentagon? In a parallelogram, adjacent angles are equal. Find the measure of all angles of this parallelogram. What is the name of this special parallelogram? A line graph which is a whole unbroken line is called a ________ graph. The standard form for 0.000064 is _______. Is it possible to have a quadrilateral in which all the angles are obtuse? Explain your answer. The area of a rhombus is 120 cm². If its one diagonal is 20 cm, find the other diagonal. What will be the side of a cube whose surface area is 2400 cm²?

Explore key geometry problems involving regular polygons, properties of parallelograms, rhombuses, and quadrilaterals. Learn how to calculate the interior angles, understand the concept of scientific notation, and find the side length of a cube given its surface area. Suitable for students in Grades 6-8.

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