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How many sides would there be in a convex polygon if the sum of all its angles is greater than 1070 degrees, but less than 1250 degrees?

 Nov 14, 2020
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How many sides would there be in a convex polygon if the sum of all its angles is greater than 1070 degrees, but less than 1250 degrees?   

 

Assuming you mean the sum of its interior angles. 

 

The formula for the sum of the interior angles of a polygon with n sides is (n – 2)(180)  

 

Divide 180 into 1070 and you get 5.944444  .....  that quotient would be (n – 2) in the formula  

 

But you can't have 0.944444 of a side, so you have to raise that quotient to 6  

 

Now (n – 2) would be 6 and so n would be 8 .....  your polygon has 8 sides  

 

Check the answer:     (8 – 2)(180) = 1080  .....  is this between 1070 and 1250?  Yes. 

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 Nov 14, 2020

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