Answers

The Brainliest Answer!
2014-10-07T19:37:58+05:30
sum of exterior angles = 360 degrees

no of sides(n) = sum of exterior angles of a regular polygon / given exterior angle of the regular polygon
⇒360/45
⇒8 sides.
no of diagonals= n(n-3)/2⇒8(8-3)/2⇒8(5)/2⇒40/2⇒20 diagonals
Therefore, number of sides are 8 and number of diagonals are 20
2 5 2
lets see
Comment has been deleted
because der shuld be at least 2 ans.
Comment has been deleted
ok
2014-10-08T12:37:20+05:30

This Is a Certified Answer

×
Certified answers contain reliable, trustworthy information vouched for by a hand-picked team of experts. Brainly has millions of high quality answers, all of them carefully moderated by our most trusted community members, but certified answers are the finest of the finest.
Please see diagram.
 
   A regular polygon has n sides and n vertices. The lines joining the vertices and the center O of polygon create n isosceles triangles. The side of the polygon becomes base of these triangles. The angle at the center in the triangle is Ф = 360°/n.
   
     As the two angles at the base are A/2 = (180° - Ф )/2.
     The interior angle at a vertex is A = 180
°Ф.
 
         So the exterior angle  is = 
Ф = 360°/n = 2π/n
              So if 360°/n = 45°,           n  = 360°/45 = 8
 
   It is a regular octagon with 8 sides.
   
   The number of line connecting each vertex to another is :  C = 8 * 7 /2  = 28.

   
  Of these, there are 8 sides among adjacent vertices.
    
        The remaining are the diagonals and are 28 – 8 = 20.
 
=========================
          n >= 3
 
   Formula for number of diagonals =  n(n-1)/2  - n = n(n-3)/2.
 
          Sum total of all exterior angles = 360° = 2 π  for any regular  polygon.
 
           One exterior angle = 360° / n = 2π/n
            one interior angle = 180° – 360°/n = 180° (n-2)/n  =  (n-2)π/n
           Angle made by a side at the cente = 360°/n  = 2π/n
           Sum total of all interior angles = n * 180° (n-2)/n  = 180° (n-2)   = (n-2)π

1 5 1