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Polygon Angles

Polygons are named based on the number of their sides, each with distinct characteristics. For instance, a triangle has 3 sides, a quadrilateral has 4, a pentagon has 5, and so on, culminating with complex names like nonagon (9 sides), decagon (10 sides), and dodecagon (12 sides). The Polygon Angle-Sum Theorem states that the sum of the interior angles of an n-gon is calculated as (n – 2) × 180 degrees. Learn how to calculate angles in polygons, including pentagons and higher n-gons.

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Polygon Angles

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  1. Polygon Angles

  2. Naming by # of sides. Polygons have specific names based on the number of sides they have: 9 – Nonagon 10 – Decagon 12 – Dodecagon n – n-gon 3 – Triangle 4 – Quadrilateral 5 – Pentagon 6 – Hexagon 8 - Octagon

  3. Polygon Angle-Sum Theorem 720° total 360° total 180° 180° 180° 180° 180° 180° 6 sides 4 triangles 4 sides 2 triangles 1080° total 180° 180° 180° 180° 180° 180° 8 sides 6 triangles

  4. Polygon Angle-Sum Theorem The sum of the measures of the angles of an n-gon is: (n – 2) x 180. How many degrees in a pentagon? (5 – 2) x 180 = 3 x 180 = 540° How many degrees in a 25-gon? (25 – 2) x 180 = 23 x 180 = 4140°

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