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salantis [7]
3 years ago
10

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

Mathematics
1 answer:
Inessa05 [86]3 years ago
7 0

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°.

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