Anonymous
Anonymous asked in Science & MathematicsMathematics · 1 month ago

# Math Exercise? Relevance

The formula to find the sum of interior angles of a polygon is 180 ( n − 2 ) where n is the number of sides.   If you want to know how that formula is gotten let me know.

Let's set up the equation.

180 ( n − 2 ) = 180 ( 2n − 2 ) - 1080

So this says for n sides, the interior angles add up to a number that when you double it to get 2n and find the sum of the interior angles  and subtract 1080 you get the same number as 180 ( n − 2 ).  now we just use algebra to solve.

180 ( n − 2 ) = 180 ( 2n − 2 ) - 1080

180n − 360 = 360n − 360 - 1080

1080 = 180n

6 = n

So a hexagon.

Let's check.  sum of interior angles of a hexagon is 180 ( 6 − 2 ) = 720  Double the number of sides to an 12 gon and the sum is 180 ( 12 − 2 ) = 1800.  Now 1800 should be 1080 more than 720.  Is it?  720 + 1080 = 1800.  Yes it is!  So there's the answer.

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