Podcast
Questions and Answers
An exterior angle of a polygon is formed by one side of the polygon and the extension of an adjacent ______.
An exterior angle of a polygon is formed by one side of the polygon and the extension of an adjacent ______.
side
The measure of an exterior angle is equal to the sum of the measures of the two non-adjacent ______ angles.
The measure of an exterior angle is equal to the sum of the measures of the two non-adjacent ______ angles.
interior
For any polygon, the exterior angle is equal to the sum of the interior angles not ______ to it.
For any polygon, the exterior angle is equal to the sum of the interior angles not ______ to it.
adjacent
To find an exterior angle of a regular polygon, use the formula: Exterior Angle = ______.
To find an exterior angle of a regular polygon, use the formula: Exterior Angle = ______.
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The sum of all exterior angles in a polygon is always ______ degrees.
The sum of all exterior angles in a polygon is always ______ degrees.
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Study Notes
Exterior Angles
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Definition: An exterior angle of a polygon is formed by one side of the polygon and the extension of an adjacent side.
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Properties:
- The measure of an exterior angle is equal to the sum of the measures of the two non-adjacent interior angles (remote interior angles).
- Each exterior angle and its corresponding interior angle are supplementary, meaning they add up to 180 degrees.
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Exterior Angle Theorem:
- For any polygon, the exterior angle is equal to the sum of the interior angles not adjacent to it.
- If there are ( n ) sides in a polygon, the sum of all exterior angles is always 360 degrees, regardless of the number of sides.
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Calculating Exterior Angles:
- To find an exterior angle of a regular polygon:
- Use the formula: ( \text{Exterior Angle} = \frac{360}{n} )
- Where ( n ) is the number of sides in the polygon.
- Use the formula: ( \text{Exterior Angle} = \frac{360}{n} )
- To find an exterior angle of a regular polygon:
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Types of Polygons:
- Regular Polygon: All sides and angles are equal, making exterior angles equal.
- Irregular Polygon: Sides and angles vary; individual exterior angles may differ.
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Applications:
- Used in geometric proofs and problem-solving.
- Important in construction and design where angles are critical.
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Example:
- For a triangle, the sum of the exterior angles is 360 degrees:
- If one exterior angle is 100 degrees, the other two can be found by using the relationship with their respective interior angles.
- For a triangle, the sum of the exterior angles is 360 degrees:
Definition of Exterior Angles
- Formed by one side of a polygon and the extension of an adjacent side.
Properties of Exterior Angles
- Measure equates to the sum of two non-adjacent interior angles (remote interior angles).
- Exterior angle and its corresponding interior angle are supplementary, totaling 180 degrees.
Exterior Angle Theorem
- For any polygon, an exterior angle equals the sum of the two non-adjacent interior angles.
- The sum of all exterior angles for any polygon is always 360 degrees, irrespective of the number of sides.
Calculating Exterior Angles
- For a regular polygon, exterior angle can be calculated using:
[ \text{Exterior Angle} = \frac{360}{n} ]
where ( n ) is the number of sides.
Types of Polygons
- Regular Polygon: All sides and angles are equal, resulting in equal exterior angles.
- Irregular Polygon: Sides and angles differ, leading to varying exterior angles.
Applications of Exterior Angles
- Fundamental in geometric proofs and problem-solving in mathematics.
- Crucial in fields like construction and design where angular measurements are vital.
Example of Exterior Angles
- In a triangle, the collective sum of exterior angles is 360 degrees.
- If one exterior angle measures 100 degrees, the other two can be determined using their interior angle relationships.
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Description
Explore the concept of exterior angles in polygons, including their properties and the Exterior Angle Theorem. This quiz covers calculations and types of polygons, providing a comprehensive understanding of this important geometric concept.
