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How Do You Find the Sum of the Interior Angles of a Polygon?

What is the formula for the sum of the interior angles for a polygon?

Summary

  1. Interior angles are the angles formed on the inside of a polygon
  2. Draw diagonals between each non-adjacent vertex
  3. Adjacent verticies are those that are right next to the original vertex
  4. We can label the angles of the two triangles we made in the 4-sided figure
  5. The Triangle Sum Theorem says that the sum of the angles of a triangle is always 180 degrees
  6. The little superscript circle means 'degrees'
  7. The little 'm' with a wedge symbol means the 'measure of an angle'
  8. 'n' stands for the number of sides of the polygon

Notes

    1. Adjacent vertices are those that are right next to the original vertex
    2. So we're just drawing diagonals across the polygons from corner to corner
    1. By this pattern, a polygon with 9 sides would have 7 triangles!
    1. Interior angles are the angles formed on the inside of a polygon
    2. The little cirlcle next to 180 means 'degrees'
    3. There are three interior angles in a triangle
    4. These three angles always add up to 180 degrees
    5. The little 'm' with a wedge symbol means the 'measure of an angle'
    1. Since there are 2 triangles in a 4 sided figure, there should be 2 sets of 3 angles to label
    2. This means that if we add up each set of angles, they will each equal 180 degrees
    1. The little circles next to 180 and 360 means 'degrees'
    2. The sum of the interior angles in the four-sided figure is 360 degrees
    1. The little circle next to 180 means 'degrees'
    2. For the 4-sided figure we'd multiply 2 by 180 degrees to get 360
    3. For the 5-sided figure we'd multiply 3 by 180 degrees to get 540
    4. For the 6-sided figure we'd multiply 4 by 180 degrees to get 720
    1. 'n' stands for the number of sides in the polygon
    2. Remember, the number of triangles is the number of sides (n) minus 2
    1. Remember, the number of triangles is the number of sides (n) minus 2
    2. The Triangle Sum Theorem says that the sum of interior angles of any triangle is 180 degrees
    3. So this formula just tells us to multiply the number of triangles by the sum of the angles of each triangle
    4. This gives us the sum of the angles of the whole polygon!