A polygon has n sides. Three of its exterior angels are 70 degrees, 80 degrees and 90 degrees. The remaining (n-3) exterior angels are each 15 degrees. How many sides does this polygon have?
2006-06-20 18:47:58 · 11 answers · asked by LaLa The Mathematician 1 in Science & Mathematics ➔ Mathematics
HINT: Try drawing the figure out and see if it is possilbe.
2006-06-20 18:53:49 · update #1
A hendecagon has all sides equal right? In this case, it does not look right.
2006-06-20 18:59:48 · update #2
Storage,
There are regular polygons, and irregular polygons.
Regular polygons have all sides equal. Irregular polygons do not (though they may have some sides equal). Many people, when they think of a hexagon automatically think of a regular hexagon, but by definition a hexagon is any six sided polygon, regular or irregular. Not all quadrilaterals are squares, similarly not all polygons are regular.
The answer is 11
The sum of the exterior angles is 360 degrees.
70+80+90 = 240 degrees
360-240 = 120 degrees
120/15 = 8
So there are 8+3 = 11 sides
2006-06-20 19:00:10 · answer #1 · answered by Jimbo 5 · 0⤊ 0⤋
The sum of exterior angles of ALL polygons is 360.
The formula is as follows:
15(n - 3) + 70 + 80 + 90 = 360
Distribute and combine
15n - 45 + 240 = 360
combine and transpose
15n = 360 - 195
combine and divide
n = 11
Therefore, the polygon has 11 sides
^_^
2006-06-20 22:11:25 · answer #2 · answered by kevin! 5 · 0⤊ 0⤋
11 sides
all of the angles have to equal 360 degrees. 70 + 80 + 90 = 240
360-240=120
120/15 = 8
8+3=11
2006-06-20 18:54:03 · answer #3 · answered by The Apple Chick 7 · 0⤊ 0⤋
I converted each exterior angle to an interior angle
110, 100, 90 and (n-3) 165.
The sum of the interior angles of an n-sided polygon is 180*(n-2)
110 +100 +90 +165*(n-3) = 180*(n-2)
300 +165*(n-3) = 180*(n-2)
300 +165n -495 = 180n -360
165 =15n
11 =n
n =11
2006-06-20 19:26:09 · answer #4 · answered by PC_Load_Letter 4 · 0⤊ 0⤋
A regular polygon is a polygon of n sides, where all the sides are the same length. For instance, an equilateral triangle is a regular polygon of 3 sides. A square is a regular polygon of 4 sides.
2016-05-20 07:59:52 · answer #5 · answered by ? 4 · 0⤊ 0⤋
360-70-80-90=120. 120/15 = 8. 8+3 =11. Eleven sides.
2006-06-20 20:53:13 · answer #6 · answered by K.J. Jeyabaskaran K 3 · 0⤊ 0⤋
central angle = exterior angles
the sum of the central angles add up to be 360
15(n - 3) + (70 + 80 + 90) = 360
15(n - 3) + 240 = 360
15(n - 3) = 120
n - 3 = 8
n - 3 = 8
n = 11
There are 11 angles.
The reason that the exterior angle equals central angle, is because the exterior angle plus the interior angle adds up to be 180. Same goes for the central angle and the interior angle.
2006-06-20 19:02:15 · answer #7 · answered by Sherman81 6 · 0⤊ 0⤋
it has 11 sides
a figure has 360 degrees. you tell us 70 80 and 90 degrees. that is 240 degrees. leaving 120 degrees, divide by 15. leaving 8 sides. 8 + 3 = 11
2006-06-20 18:52:35 · answer #8 · answered by pukcipriavroc8v 4 · 0⤊ 0⤋
11
(360-70-80-90)/15+3=11
Edit:
Mine wins cuz i got it first!!!!
2006-06-20 18:51:20 · answer #9 · answered by sk8er982002 2 · 0⤊ 0⤋
11 sides. its called hendecagon.
2006-06-20 18:56:15 · answer #10 · answered by jan rei 2 · 0⤊ 0⤋