If the sum of the measures of the interior angles of a polygon is 1920°, how many sides does it have? math

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Mathematics Thái Dương 4 years 2021-08-20T19:46:59+00:00 2021-08-20T19:46:59+00:00 1 Answers 16 views 0

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Latifah · Answer 1 · 2021-08-20T19:48:26+00:00

Answer: There is no polygon with the sum of the measures of the interior angles of a polygon is 1920°.

Step-by-step explanation:

The sum of the measures of interior angles of a polygon with $n$ sides is given by:-

$(n-2)\times180^{\circ}$

Given: The sum of the measures of the interior angles of a polygon is 1920°.

i.e. $(n-2)\times180^{\circ}=1920^{\circ}$

$n-2=\dfrac{1920}{180}\\\\ n= \dfrac{1920}{180}+2\\\\ n=\dfrac{2280}{180}=12.67$

But number of sides cannot be in decimal.

Hence, there is no polygon with the sum of the measures of the interior angles of a polygon is 1920°.