The sum of the angles of a triangle is 180
For a square it’s 360
For a pentagon it’s 540
For a hexagon it’s 720
Why is that?
In: Mathematics
The angle of a polygon is (n-2)*180, where n is the number of sides. Why?
ELI5, you can form n triangles out of any polygon by using the 2 end points of each side to the center. the center angles will total 360 therefore we get n-2.
Maybe not so ELI5: Take a pentagon. Point A is going to be the center. Point B and C are going to be the end points of a line that’s part of a hexagon. Connect all the points, what does it form? A triangle. Now make as many triangles as you can while always using point A and the end points of a line. So if B,C,D,E,F are the points at the end of a line. You have triangles ABC, ACD, ADE, AEF, AFB. 5 triangles. The total sum of those triangles is 5*180 = 900. However, that Angle A on all the triangles. If you draw it what you’ll see is it’s a perfect circle, 360 degrees, which shouldn’t be part of the sum. 900-360 = 540.
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