Math Problem Statement
Solution
Let me extract the questions from the image and solve them for you:
Questions Extracted:
- 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 is _______.
- Is it possible to have a quadrilateral in which all the angles are obtuse? Explain your answer.
- The area of a rhombus is . If its one diagonal is , find the other diagonal.
- What will be the side of a cube whose surface area is ?
Answers:
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Measure of each interior angle of a regular pentagon: The formula for the measure of an interior angle of a regular polygon is: For a pentagon (): Answer: 108°
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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 , making the parallelogram a rectangle. Answer: All angles are , and the parallelogram is a rectangle.
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A line graph which is a whole unbroken line: Answer: A continuous graph.
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Standard form of : Standard form is also known as scientific notation. We move the decimal point 5 places to the right: Answer: .
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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 . An obtuse angle is greater than . If all four angles were obtuse, their sum would exceed , which is not possible. Answer: No, it is not possible.
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Find the other diagonal of a rhombus: The area of a rhombus is given by: where and are the diagonals. Given: Substituting into the formula: Solving for : Answer: The other diagonal is .
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Find the side of a cube with a surface area of : The surface area of a cube is given by: where is the side length of the cube. Given: Solving for : Taking the square root: Answer: The side length is .
Let me know if you want more details or explanations on any of these answers. Here are 5 related questions to consider:
- What is the sum of interior angles of a regular hexagon?
- How do you calculate the exterior angle of any regular polygon?
- What are the properties of a rhombus in relation to its diagonals?
- Can a quadrilateral have exactly two obtuse angles? Why or why not?
- How do you convert a number like into standard form?
Tip: Always remember that the sum of interior angles in any polygon is given by , where is the number of sides.
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Math Problem Analysis
Mathematical Concepts
Geometry
Polygons
Angles
Graphs
Scientific Notation
Properties of Quadrilaterals
Surface Area
Diagonals
Formulas
Interior angle of a regular polygon: (n-2) × 180° / n
Area of a rhombus: (1/2) × d1 × d2
Surface area of a cube: 6s²
Theorems
Properties of Parallelograms
Angle Sum Property of Quadrilaterals
Definition of Scientific Notation
Suitable Grade Level
Grades 6-8
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