The measure of an exterior angle of an equiangular polygon is twice that of an interior angle. What is the name of the polygon?
- I know I have to find the number of sides to determine that
- The formula for finding exterior angles is 360/n (number of sides)
Please help and thank you so much!
2007-01-30 14:06:18 · 5 answers · asked by ♫ singin_gurl1200 ♫ 3 in Science & Mathematics ➔ Mathematics
3x=180
x=60 interior angle
360/n=120
n=3
triangle
2007-01-30 14:12:11 · answer #1 · answered by iyiogrenci 6 · 1⤊ 0⤋
There is only one equiangular polygon for which the exterior angle is more than the interior angle, and that's for a triangle. (think about a square/rectangle, for which the exterior angle will be 90* as will the interior angle, and for any polygon with more sides, the exterior angle will only decrease.)
Given the interior angles of a regular triangle will always be 60, the exterior will be 360/3 = 120. 60 is half 120.
So the answer is a triangle.
2007-01-30 22:15:38 · answer #2 · answered by J 2 · 0⤊ 0⤋
OK, so I figure that if the number of degrees in any polygon is (n-2)180 where n is the number of sides.Tthen in an equiangular polygon the number of degrees in one angle would be the above expression divided by the number of sides or n.
360/n = 2(n-2)180/n which works out (I think) to be n=3 which is our friendly triangle....
Does that sound about right?
2007-01-30 22:15:06 · answer #3 · answered by SBT 1 · 0⤊ 0⤋
equilateral triangle. Interior angle=60, exterior=120
2007-01-30 22:13:43 · answer #4 · answered by algebraman 1 · 0⤊ 0⤋
Interior Angles = 180(n - 2)/n
Exterior Angles = 360/n
360/n = 2(180(n - 2)/n)
360/n = (360/n)(n - 2)
1 = n - 2
n = 3
ANS : Triangle
Interior Angles total to be 180
Exterior Angles total to be 360
2007-01-30 22:55:29 · answer #5 · answered by Sherman81 6 · 0⤊ 0⤋