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Polygons: Formula and Examples
Exterior Angles and Interior Angles
Interior Angle Sum Theorem
The sum of the measures of the interior angles of a polygon with n sides is (n-2)180
Examples:
- Triangle or ( '3-gon'
)
- sum of interior angles: (3-2) 180 = 180°
- Quadrilateral which has four sides ( ' 4-gon')
- sum of interior angles: (4-2)180 = 360°
- Hexagon which has six sides ( '6-gon')
- sum of interior angles: (6-2)180 = 720°
In order to find the measure of a single interior angle of a regular polygon (a polygon with sides of equal length and angles of equal measure) with n sides, we just divide the sum of the interior angles or (n-2) × 180 by the number of sides or n
An interior angle of a regular polygon with n sides is  Example: To find the measure of an interior angle of a regular octagon, which has 8 sides, apply the formula above as follows:
( (8-2) × 180) /8 = 135°
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What is the total number degrees of all interior angles of a triangle?
180°
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What is the total number of degrees of all interior angles of the polygon on the left?
360° since the polygon on the left is really just two triangles and each triangle has 180°. |
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What is the sum measure of the interior angles of the polygon (a pentagon) on the left?
Use Interior Angle Theorem: (5-2)× 180= 3× 180= 540°.
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What is sum measure of the interior angles of the polygon (a hexagon) on the left?
Use Interior Angle Theorem: (6-2)× 180= 4 × 180 = 720°.
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Exterior Angle of a Polygon | Interior Angle Sum Theorem
The sum of the measures of the exterior angles of a polygon, one at each vertex, is 360°.
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