A polygon has n sides. Two of its interior angles are 50 degrees and 30 degrees while the remaining interior angles are each equal to 164 degrees. Find n.
2006-07-02 18:57:45 · 8 answers · asked by LaLa The Mathematician 1 in Science & Mathematics ➔ Mathematics
The answer is 7.
2006-07-02 19:07:07 · answer #1 · answered by -KJ- 3 · 2⤊ 3⤋
The sum of the interior angles for an n-gon is (n-2)180°. The sum of the angles in your polygon is 50°+30°+164(n-2)°. Set these equal to each other - then (n-2)180=(n-2)164+80 â (n-2)16=80 â n-2=5 â n=7
2006-07-03 02:05:22 · answer #2 · answered by Pascal 7 · 0⤊ 0⤋
There are two ways to get the solution for this question..
>>>First is though interior angles...
Formula for sum of interior angles... (n-2) x 180º....
Since two of its interior angles are 50º and 30º...
Sum will be 80º...
Sum of remaining angles (n-2) with interior angles of 164º can be written as...
(n-2) x 164º...
Thus, an equation can be formed...
(n-2) x 180º = 80º + (n-2) x 164º
180ºn - 360º = 80º + 164ºn - 328º
180ºn - 164ºn = 360º + 80º - 328º
16ºn = 112º
n = 112º / 16º = 7
Therefore the polygon has 7 sides....
>>>Another method is by exterior angles..
Sum of all exterior angles is 360º...
The first two angles given will have exterior angles of 130º and 150º respectively... (calculated by subtracting with 180º)
The remaining angles (n-2) will have external angles of 16º each... (180º - 164º)
Therefore, an equation can be formed...
130º + 150º + (n-2)x16º = 360º
(n-2)x16º = 360º - 130º - 150º
16ºn - 32º = 80º
16ºn = 80º + 32º
16ºn = 112º
n = 112º/16º = 7
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There is another simpler working to calculate based on exterior angles...
Minus away the two known exterior angles...
360º - 130º - 150º = 80º
Find the remaining number of sides by dividing it...
80º / 16º = 5
5 is the remaining angles and since you also have another 2 angles.. total number of sides of polygon is 7... (5 + 2)...
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As you can see... Whatever methods you use, it will give you the same answer..
In other words, there is no doubt that you have got the correct answer..
A 7-sided polygon is called a heptagon...
Cheers.. (",)
2006-07-03 03:10:05 · answer #3 · answered by Ellusive Lady 3 · 0⤊ 0⤋
You see, the first two exterior angles are 130 deg and 150 deg, adding up to 280 deg.
Then, you know a polygon has total sum of exterior angles of 360 deg.
Sum of remaining exterior angles = 360 - 280 = 80 deg
The exterior angle for the 164 deg interior angles is 180 - 164 = 16.
80 / 16 = 5
Thus there are 5 more sides in addition to the first two sides.
Therefore there are 7 sides.
2006-07-03 02:24:44 · answer #4 · answered by tan 3 · 0⤊ 0⤋
the polygon has 7 sides,
80 + 164n until you get a number which equals an angle sum.
so 80 + 164 + 164 + 164+ 164+164 = 900
= 7 sides
2006-07-03 02:09:18 · answer #5 · answered by cool_person 2 · 0⤊ 0⤋
10, The sum of angle in polygon is equal to n x 90 degree
so in this case : n = ((164 x 5) + 30 + 50) / 90 = 10
2006-07-03 02:14:47 · answer #6 · answered by qwerty 1 · 0⤊ 0⤋
its a pentagon :p WOZ apiece of CAKE, yeah 5 sides
2006-07-03 02:04:36 · answer #7 · answered by Anonymous · 0⤊ 0⤋
HEPTAGON
2006-07-03 06:30:03 · answer #8 · answered by nithin 1 · 0⤊ 0⤋