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Questions and Answers
How many sides does a regular polygon have if its interior angle measures 120°?
How many sides does a regular polygon have if its interior angle measures 120°?
6 sides
How many sides does a polygon have if the sum of interior angles is 1980°?
How many sides does a polygon have if the sum of interior angles is 1980°?
13 sides
How many sides does a polygon have if the sum of interior angles is 900°?
How many sides does a polygon have if the sum of interior angles is 900°?
7 sides
How many sides does a regular polygon have if its exterior angle is 90°?
How many sides does a regular polygon have if its exterior angle is 90°?
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What is x if each interior angle of a regular pentagon measures 2x + 4°?
What is x if each interior angle of a regular pentagon measures 2x + 4°?
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What is the measure of the remaining angle if the exterior angles of a pentagon are 57°, 74°, 56°, and 66°?
What is the measure of the remaining angle if the exterior angles of a pentagon are 57°, 74°, 56°, and 66°?
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How many sides must a regular polygon have if a measure of an interior angle is 162°?
How many sides must a regular polygon have if a measure of an interior angle is 162°?
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What is the sum of the interior angles of an 11-gon?
What is the sum of the interior angles of an 11-gon?
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What is the measure of an exterior angle for a regular octagon?
What is the measure of an exterior angle for a regular octagon?
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What is the measure of an exterior angle of a regular decagon?
What is the measure of an exterior angle of a regular decagon?
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How many sides does a regular polygon have if the exterior angle measures 40°?
How many sides does a regular polygon have if the exterior angle measures 40°?
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What is the name of a polygon that has 9 sides?
What is the name of a polygon that has 9 sides?
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How many sides does a polygon have if it has an interior angle sum of 2520°?
How many sides does a polygon have if it has an interior angle sum of 2520°?
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What is the measure of an interior angle of a regular 360-gon?
What is the measure of an interior angle of a regular 360-gon?
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How many sides does a polygon have if its interior angle sum is 720°?
How many sides does a polygon have if its interior angle sum is 720°?
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A polygon has an interior angle sum of 540°. How many sides does it have?
A polygon has an interior angle sum of 540°. How many sides does it have?
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A polygon has an interior angle sum of 360°. How many sides does it have?
A polygon has an interior angle sum of 360°. How many sides does it have?
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A polygon has an interior angle sum of 180°. How many sides does it have?
A polygon has an interior angle sum of 180°. How many sides does it have?
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A polygon has an interior angle sum of 900°. How many sides does it have?
A polygon has an interior angle sum of 900°. How many sides does it have?
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A polygon has an interior angle sum of 1080°. How many sides does it have?
A polygon has an interior angle sum of 1080°. How many sides does it have?
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A polygon has an interior angle sum of 1260°. How many sides does it have?
A polygon has an interior angle sum of 1260°. How many sides does it have?
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A polygon has an interior angle sum of 1440°. How many sides does it have?
A polygon has an interior angle sum of 1440°. How many sides does it have?
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What is the name of a polygon that has 5 sides?
What is the name of a polygon that has 5 sides?
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What is the name of a polygon that has 6 sides?
What is the name of a polygon that has 6 sides?
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What is the name of a polygon that has n sides?
What is the name of a polygon that has n sides?
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What is the name of a polygon that has 7 sides?
What is the name of a polygon that has 7 sides?
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What is the name of a polygon that has 8 sides?
What is the name of a polygon that has 8 sides?
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What is the name of a polygon that has 10 sides?
What is the name of a polygon that has 10 sides?
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What is the measure of an interior angle of a regular nonagon?
What is the measure of an interior angle of a regular nonagon?
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What is the measure of an interior angle of a regular pentagon?
What is the measure of an interior angle of a regular pentagon?
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What is the measure of an interior angle of a regular hexagon?
What is the measure of an interior angle of a regular hexagon?
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What is the measure of an interior angle of a regular heptagon?
What is the measure of an interior angle of a regular heptagon?
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What is the measure of an interior angle of a regular octagon?
What is the measure of an interior angle of a regular octagon?
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What is the measure of an interior angle of a 100-gon?
What is the measure of an interior angle of a 100-gon?
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What is the measure of an interior angle of a decagon?
What is the measure of an interior angle of a decagon?
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How many sides does a regular polygon have if its interior angle is 140°?
How many sides does a regular polygon have if its interior angle is 140°?
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What is the measure of an interior angle of a 15-gon?
What is the measure of an interior angle of a 15-gon?
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What is the measure of an exterior angle of a 10-gon?
What is the measure of an exterior angle of a 10-gon?
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How many sides must a regular polygon have if the measure of an interior angle is 162°?
How many sides must a regular polygon have if the measure of an interior angle is 162°?
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If the measure of an exterior angle of a regular polygon is 15°, how many sides does it have?
If the measure of an exterior angle of a regular polygon is 15°, how many sides does it have?
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What is the measure of an interior angle of a regular 24-gon?
What is the measure of an interior angle of a regular 24-gon?
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Study Notes
Properties of Polygons
- A regular polygon with an interior angle of 120° has 6 sides.
- The sum of the interior angles of a polygon can be used to find the number of sides. For example, a sum of 1980° corresponds to 13 sides.
- A polygon with a sum of interior angles equal to 900° has 7 sides.
Exterior Angles
- An exterior angle of a regular polygon measures 90° indicates it has 4 sides.
- The measure of an exterior angle can also determine the number of sides. For example, an exterior angle of 40° means the polygon has 9 sides.
- Exterior angles for regular polygons:
- Decagon: 36°
- Octagon: 45°
Interior Angles
- Internal angle properties differ with the number of sides:
- Regular pentagon: Each angle is 108°.
- Regular hexagon: Each angle is 120°.
- Regular heptagon: Each angle is approximately 128.57°.
- Regular octagon: Each angle is 135°.
- Regular nonagon: Each angle is 140°.
- Regular decagon: Each angle is 144°.
- Regular polygon with 360 sides: Each angle is 179°.
- Regular 15-gon: Each angle is 156°.
Polygon Names
- A 5-sided polygon is called a pentagon.
- A 6-sided polygon is a hexagon.
- A 7-sided polygon is known as a heptagon.
- An 8-sided polygon is referred to as an octagon.
- A 9-sided polygon is called a nonagon.
- A 10-sided polygon is classified as a decagon.
- A polygon with 'n' sides is generally referred to as an n-gon.
Angle Sums and Sides
- The sum of the interior angles formula is used to find sides:
- 360° sum: 4 sides (quadrilateral)
- 540° sum: 5 sides (pentagon)
- 720° sum: 6 sides (hexagon)
- 900° sum: 7 sides (heptagon)
- 1080° sum: 8 sides (octagon)
- 1260° sum: 9 sides (nonagon)
- 1440° sum: 10 sides (decagon)
- 2520° sum: 16 sides.
Angle Relationships
- Each interior angle can be calculated based on the formula related to sides.
- Regular polygons have consistent angle measurements that can be used to determine the polygon type and its properties.
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Description
Test your knowledge on the properties of polygons, focusing on interior angles, exterior angles, and the corresponding number of sides. This quiz features various scenarios where you will calculate the number of sides based on given angle measures. Perfect for students studying geometry!
