MathematicsThe total measurement of all the interior angles of a regular polygon is equal to 10 right angle. Find out which Kind of polygon it is.

The total measurement of all the interior angles of a regular polygon is equal to 10 right angle. Find out which Kind of polygon it is.


  1. A
    Decagon
  2. B
    Hexagon
  3. C
    Pentagon
  4. D
    Heptagon 

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    Solution:

    Let the polygon be on the n-side. It has n interior angles
    we know that the sum of all the interior angles of n sided regular polygon is (n – 2) π
    So, each interior angle becomes  we know that the sum of all exterior angles is 2π which is independent of the side number of a polygon?.
    It's given that the total measurement of all the interior angles of the n-sided regular polygon  is equal to 10 right angles.
    10 right angle are equal to
    = 5π
    Now, we equate the linear function of n with 5π .
    so. (n – 2) π = 5π
    n – 2 = 5
    n = 5 + 2
    n = 7
      
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