Math True Or False Question?

The sum of the all the angles in a regular polygon are always 360 degrees.








IS THAT TRUE?Math True Or False Question?
Hi,





That statement is false.





An equilateral triangle is a regular polygon with only 180 degrees.





A square is a regular polygon that does have 360 degrees.





A regular pentagon has 540 degrees.





The sum of the angles in a regular polygon with ';n'; sides is 180(n - 2) degrees, so as ';n'; increases, the sum of the angles will continue to increase as well.





However, if you look at the sum of the exterior angles for a regular polygon (or any other convex polygon) where you look at one exterior angle at each vertex, then the sum of the exterior angles is always 360 degrees, regardless of the number of sides.





n . name of regular polygon . interior angle . exterior angle . sum of exterior angles (n x exterior)


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3 . . equilateral . . . . . . . . . . . . . . . 60 . . . . . . . . . 120 . . . . . 3 x 120 = 360


4 . . . . square . . . . . . . . . . . . . . . .90 . . . . . . . . . . 90. . . . . .4 x 90 = 360


5 . . . pentagon . . . . . . . . . . . . . . 108 . . . . . . . . . . 72. . . . . .5 x 72 = 360


6 . . . hexagon . . . . . . . . . . . . . . .120 . . . . . . . . . . 60. . . . . .6 x 60 = 360


10 . . .decagon . . . . . . . . . . . . . . .144 . . . . . . . . . . 36. . . . . 10 x 36 = 360





I hope that helps!! :-)Math True Or False Question?
False.





The sum of the all 'Exterior' angles in a regular polygon are always 360 degree.