A polygon has n sides. Three of its exterior angles are 70, 80 and 90 degrees. The remaining (n-3) exterior angles are each 15 degrees. How many sides does this polygon have?
2006-07-02 19:18:25 · 6 answers · asked by LaLa The Mathematician 1 in Science & Mathematics ➔ Mathematics
The answer is either 4, 6, 8 or 7...
=)
2006-07-02 19:19:44 · answer #1 · answered by -KJ- 3 · 2⤊ 4⤋
N15+90+80+70=360
N=11
2006-07-03 05:10:27 · answer #2 · answered by Anonymous · 0⤊ 0⤋
Sum of exterior angles so far = 70 + 80 + 90 = 240 deg
Remaining sum of exterior angles = 360 - 240 = 120 deg
Remaining no. of sides = 120 / 15 = 8
Total no. of sides = 8 + 3
= 11
2006-07-03 02:28:28 · answer #3 · answered by tan 3 · 0⤊ 0⤋
Since the sum of ext. angles of any polygon is 360, then
70 + 80 + 90 + 15(n - 3) = 360
70 + 80 + 90 + 15n - 45 = 360
15n = 165
n = 11
Therefore, the polygon has 11 sides.
^_^
2006-07-03 07:20:58 · answer #4 · answered by kevin! 5 · 0⤊ 0⤋
Simple...
Sum of all exterior angles = 360º.
Since you already know 3 exterior angles, find the sum of remaining angles...
360º - 70º - 80º - 90º = 120º
Next clue given was that the remaining exterior angles are each 15º...
Therefore....
120º / 15º = 8
Meaning.. 8 sides of the polygon has an external angle of 15º...
Total sides = 8 + 3 = 11
The name for an 11-sided polygon will be hendecagon...
Cheers... (",)
2006-07-03 02:54:33 · answer #5 · answered by Ellusive Lady 3 · 0⤊ 0⤋
its a hexagon. guess only
2006-07-03 02:21:36 · answer #6 · answered by savio 4 · 0⤊ 0⤋