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Questions and Answers
What is the sum of interior angles of a polygon with 12 sides?
What is the measure of each interior angle of a regular octagon?
What is the sum of the remote interior angles of an exterior angle of a regular pentagon?
What is the relationship between an interior angle and its adjacent exterior angle of a polygon?
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What is the sum of exterior angles of a polygon with 15 sides?
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In a convex quadrilateral, the sum of an exterior angle and its adjacent interior angle is always:
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What is the relationship between the interior and exterior angles of a polygon?
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What is the sum of the exterior angles of a convex hexagon?
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In a regular polygon, what is the relationship between the measure of an interior angle and its adjacent exterior angle?
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What is the sum of the interior angles of a convex nonagon?
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Study Notes
Interior and Exterior Angles
Interior Angles
- Defined as the angles formed inside a polygon by two adjacent sides
- The sum of interior angles of a polygon with n sides is (n-2) × 180°
- Each interior angle of a regular polygon is equal to (n-2) × 180° / n
- Interior angles are always less than 180°
Exterior Angles
- Defined as the angles formed outside a polygon by one side and an extension of the adjacent side
- The sum of exterior angles of a polygon is always 360°
- Each exterior angle of a regular polygon is equal to 360° / n
- Exterior angles are always less than 180°
Relationships between Interior and Exterior Angles
- The sum of an interior angle and its adjacent exterior angle is always 180°
- An exterior angle is equal to the sum of the remote interior angles (the interior angles not adjacent to the exterior angle)
Interior Angles
- Defined as angles formed inside a polygon by two adjacent sides
- Sum of interior angles in a polygon with n sides is (n-2) × 180°
- Each interior angle in a regular polygon is (n-2) × 180° / n
- Interior angles are always less than 180°
Exterior Angles
- Defined as angles formed outside a polygon by one side and an extension of the adjacent side
- Sum of exterior angles in a polygon is always 360°
- Each exterior angle in a regular polygon is 360° / n
- Exterior angles are always less than 180°
Relationships between Interior and Exterior Angles
- Sum of an interior angle and its adjacent exterior angle is always 180°
- Exterior angle equals the sum of the remote interior angles (interior angles not adjacent to the exterior angle)
Interior Angles
- Interior angles are formed inside a polygon by two adjacent sides
- The sum of interior angles of a polygon with n sides is (n-2) × 180°
- Each interior angle of a regular polygon is equal to (n-2) × 180° / n
- Interior angles are always less than 180°
Exterior Angles
- Exterior angles are formed outside a polygon by one side and an extension of the adjacent side
- The sum of exterior angles of a polygon is always 360°
- Each exterior angle of a regular polygon is equal to 360° / n
- Exterior angles are always less than 180°
Relationships between Interior and Exterior Angles
- The sum of an interior angle and its adjacent exterior angle is always 180°
- An exterior angle is equal to the sum of the remote interior angles (the interior angles not adjacent to the exterior angle)
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Description
Learn about interior and exterior angles of polygons, including their definitions, sum, and properties.
