Center Focus

Shapes and Angles

  1. Have your students figure out the sum of the angles of a rectangle. Give them this reproducible that explains why the angles of a four-sided figure will always add up to 360 degrees.
  2. Based on this reasoning, have your students figure out the sum of angles of other shapes, i.e. pentagon, hexagon, dodecahedron.
  3. These shapes are all regular shapes--the interior angles are equal and the lengths of the sides are equal. As your students experiment with figures that have unequal angles/sides, they will realize that all four-sided figures have interior angles that sum to 360 degrees. Likewise, all eight-sided figures have interior angles that add up to 1080 degrees.
  4. In order to help your students prove this, have them measure the angles of a 5-pointed star using a protractor. Download a five-pointed star here. They should add up the angles (10 of them); the sum will be 1440. You may want to have them continue doing this with other shapes to further their understanding.
  5. This download should be helpful for this activity. It is a list of shapes, from 4-sided to 12-sided, and the sum of their angles.

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