Question

Is it possible to have a regular polygon each of whose interior angle is 55 degree.

Answer 1

Answer:

Step-by-step explanation:

It impossible for a interior angle of a regular polygon to equal degrees. ... The sum of the exterior angles of any polygon is degrees, so the number of sides would be supposedly equal to or . A polygon cannot have sides, so the angle can't measure degrees.

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Answer 2

It is not possible to have a polygon with 55° as each interior angle

Given:

Is it possible to have a regular polygon each of whose an interior angle is 55 degrees?    

Solution:

Formula used:

Sum of interior angle = (n-2) x 180°

Where 'n' is the number of sides

Let's assume that the regular polygon has n sides and each interior angle is 55 degrees.  

The sum of the interior = 55n    

Using the above formula,

Sum of interior angles = (n - 2)×180°  

Hence, 55n = (n - 2)(180°)

=> 11n = (n - 2)36

=> 11n = 36n - 72

=> 36n - 11n  = 72

=>  25n = 72

=> n = 2.88

Here the number of sides came out to a decimal number which is not possible  

Therefore,

It is not possible to have a polygon with 55° as each interior angle

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