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?

Guest 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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Guest Nov 14, 2020