Question

if the sum of angle of any polygon is 2000. why​

Answer 1

SOLUTION

CORRECT QUESTION

Is 2000° , the sum of the angle of a polygon ? why ?

EVALUATION

If possible 2000° is the sum of all angle of a n sided polygon

Number of sides = n

Sum of angles

$\displaystyle \sf{ = (n - 2) \times {180}^{ \circ} }$

So by the given condition

$\displaystyle \sf{ (n - 2) \times {180}^{ \circ} = {2000}^{ \circ} }$

$\displaystyle \sf{ \implies (n - 2) = \frac{ {2000}^{ \circ} }{ {180}^{ \circ}} }$

$\displaystyle \sf{ \implies (n - 2) = \frac{200 }{ 18} }$

$\displaystyle \sf{ \implies (n - 2) = \frac{100 }{9} }$

$\displaystyle \sf{ \implies n = \frac{100 }{9} + 2 }$

$\displaystyle \sf{ \implies n = \frac{100 + 18 }{9} }$

$\displaystyle \sf{ \implies n = \frac{118 }{9} }$

Which is not a natural number

Hence it is not possible 2000° as the sum of the angle of a polygon

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