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Problem 6

Sum of Angles of Polygon. . The sum of the angles of the polygon to the right is

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Problem 6

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    1. Problem 6 By: Jeremy Duggan

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    4. “Let’s try to derive a formula for the sum of the interior angles for a convex polygon with any number of sides.” “First let’s make a polygon with “n” number of sides and “n” number of angles.” Draw the polygon and label the angles. “Then pick an angle.” Highlight angle 4 “From that angle, draw a line connecting it to every non-adjacent angle, which will create (n-2) triangles.” Draw lines connecting angle 1 to all the other non-adjacent angles. “Remember that a triangle’s interior angles have a sum of 180 degrees.” “Add up the interior angles of the triangles that were created when angle 4 was connected to every non-adjacent angle.” Put 180° into each triangle. Add the 180° from each triangle together. “You will then have to add 180° to itself “n-2” times. “We can then rewrite the formula as (n-2)180 Draw =(n-2)(180).“Let’s try to derive a formula for the sum of the interior angles for a convex polygon with any number of sides.” “First let’s make a polygon with “n” number of sides and “n” number of angles.” Draw the polygon and label the angles. “Then pick an angle.” Highlight angle 4 “From that angle, draw a line connecting it to every non-adjacent angle, which will create (n-2) triangles.” Draw lines connecting angle 1 to all the other non-adjacent angles. “Remember that a triangle’s interior angles have a sum of 180 degrees.” “Add up the interior angles of the triangles that were created when angle 4 was connected to every non-adjacent angle.” Put 180° into each triangle. Add the 180° from each triangle together. “You will then have to add 180° to itself “n-2” times. “We can then rewrite the formula as (n-2)180 Draw =(n-2)(180).

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