Mathematics
Grade9
Easy

Question

The sum of interior angles of an octagon is __________.

  1. 360 degree
  2. 1080 degree
  3. 720 degree
  4. 900 degree

hintHint:

Polygon is a two- dimensional closed figure which is made up of three or more line segments. Each polygon has its own properties based on the number of sides. Here, we have to find the sum of all the angles of the given polygon.

The correct answer is: 1080 degree


    In the question it is given that we have to find the sum of all the angles of an octagon.
    text  The sum of angles of a n-gon=  end text 180 degree cross times left parenthesis n minus 2 right parenthesis
space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space w h e r e comma space n equals space n u m b e r space o f space s i d e s space o f space t h e space p o l y g o n
text  The sum of angles of an octagon = end text 108 cross times left parenthesis 8 minus 2 right parenthesis degree space space space space space space space space space space space space space space space space space space space space space space space space left parenthesis H e r e comma space n equals 8 right parenthesis
space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals left parenthesis 180 cross times 6 right parenthesis degree
space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals 1080 degree
    So, the sum of all the angles of an octagon is 1080 degree.
    Therefore, the correct option is b, i.e., 1080 degree.

    Octagon is an eight sided polygon whose sum of all angles can be determined using the formula: S u m space o f space a l l space a n g l e s space o f space a space p o l y g o n equals 180 degree cross times left parenthesis n minus 2 right parenthesis, where n is the number of sides of the polygon.

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