# The sum of the interior angles of a triangle is 180º; of a quadrilateral is 360º and of a pentagon is 540º. Assuming this pattern continues, what is the sum of the interior angles of a 10-sided polygon?

2
by cessty

2015-07-24T19:39:23+08:00
The sum of the interior angles of a decagon is 1440°C.. you can get it by the formula (n-2) 180.. n being the sides of the polygon..
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2015-07-24T19:42:45+08:00
A traingle has 3 sides with 180 degress.
To get the "pattern" you need to Mathematically understand it.
A Quadrilateral has 4 sides with 360 degrees.
But a Quadrilateral may be divided into 2 triangles.
A triangle is 180 degress; 2 triangles are 360 degrees.
A pentagon has 5 sides with 540 degrees
But it can be formulated into 3 triangles.
3 x 180 = 540
Looking at the pattern, 3 sides is formulated into 1 traingle. 4 sides but can be formulated into 2 traingles. 5 sides but can be formulated into 3 traingles.
3 - 1 = 2
4 - 2 = 2
5 - 3 = 2
Plus multiplying each by 180, will give the proper sum of all interior angles, depending on the number of sides.
So, the formula is (n-2) 180 degrees.
Note: Use n as the number of sides of the polygon..
So a 10 sided polygon will have 1440 degrees.