SOLUTION: In a regular polygon, each angle is n degree. The number of angles in such a polygon is A)180/n+2 B)360/180-n C) 90/n+2 D)360/180+n E)180(n+2)/n

Algebra ->  Polygons -> SOLUTION: In a regular polygon, each angle is n degree. The number of angles in such a polygon is A)180/n+2 B)360/180-n C) 90/n+2 D)360/180+n E)180(n+2)/n      Log On


   

Question 1125556: In a regular polygon, each angle is n degree. The number of angles in such a polygon is
A)180/n+2
B)360/180-n
C) 90/n+2
D)360/180+n
E)180(n+2)/n
Found 2 solutions by MathLover1, ikleyn:
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
The sum of the interior angles, in degrees, of a regular polygon is given by the formula 180%28n-2%29, where n is the number of sides.

Shape.........|the number of sides..........Sum of Interior Angles.....|Each Angle
Any Polygon| .............. n....... | ..................... 180%28n-2%29° |............. ....... 180%28n+-2%29%2Fn.......

Answer by ikleyn(52803) About Me  (Show Source):
You can put this solution on YOUR website!
.
Let the number of angles be " m ".  It is the same as the number of sides.


Then  


    m*n = 180*(m-2)   degrees,

    mn = 180m - 360

    360 = 180m - mn

    360 = m*(180-n)

    m = 360%2F%28180-n%29.


Answer.    Option B) of the list.