SOLUTION: The sum of all but one of the angles of a particular convex polygon is 1578 degrees. What is the measure, in degrees, of the remaining interior angle?
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Question 949307: The sum of all but one of the angles of a particular convex polygon is 1578 degrees. What is the measure, in degrees, of the remaining interior angle?
Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
The measure of each (interior) angle in a convex polygon is less than .
The sum of the measures of all the (interior) angles of a convex polygon with sides is
Since and ,
we know that the polygon must have at least
<---> sides.
Could it have <---> ?
That would make the sum of the measures of all its angles at least
, and then, the measure of the remaining interior angle would be at least
.
Then, <---> ,
and the sum of the measures of all the (interior) angles is
.
The measure of the remaining interior angle is
.
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