It is possible for the interior angles of a regular polygon to measure 145°?
Give support to your answer
2006-07-19 21:02:30 · 6 answers · asked by Zman 1 in Science & Mathematics ➔ Mathematics
hmm
2006-07-19 21:05:34 · answer #1 · answered by Anonymous · 0⤊ 0⤋
Not in plane geometry. The total of the interior angles is 180 degrees times (two less than the number of angles). There is no integer which, when multiplied by 180, gives 145.
But that answer applies to the total of the interior angles. When considering whether individual interior angles can be 145 degrees, we want to see if we can find an integer n [number of vertices] such that n * 145 = (n - 2) * 180. The equation has a solution, but the solution is not an integer. Hence it is not possible.
2006-07-19 21:22:23 · answer #2 · answered by Anonymous · 0⤊ 0⤋
No. A regular polygon has a number of sides:
sides = 360/(180-x)
where x is the interior angle. Therefore, if x is 145, the number of sides is not an integer and it doesn't work.
2006-07-19 21:05:46 · answer #3 · answered by Steve W 3 · 0⤊ 0⤋
145 = (180(n - 2))/n
145n = 180n - 360
-35n = -360
n = (360/35)
n = (72/7)
ANS : No, because you will get a fraction of an angle.
2006-07-20 03:58:08 · answer #4 · answered by Sherman81 6 · 0⤊ 0⤋
no, because a triangle has atleast 180
2006-07-19 21:05:48 · answer #5 · answered by Anonymous · 0⤊ 0⤋
I dont know actually, I suck big time at math especially Trigonometry, sorry about that^^
2006-07-19 21:05:11 · answer #6 · answered by Kent Ishii 2 · 0⤊ 0⤋