Geometry Question Help! Convex polygon?

Question

Well can't find answer to this geometry problem, that is hunting me down!

How many sides does a convx polygon have when the sum of measure of all but one of its interior angles is 3080

Plz help

Answer 1

A convex polygon has all angles less than 180 degrees.
NOw think a triangle has 3 sides or 180 degrees
a quad. has 4 sides and 360 degrees or 2(180)
A PENTAGON 5 sides and 50 degees or 3(180)
AND SO ON...
You should notice that the sum is always a multiple of 180
but 3080 is not a multiple of 180 . 18 times 180 is 3240 which is the next closest multiple ( The missing angle is 3240 - 3080 or 160 degees... but I digress!)
From the opening, you should also notice the multiple plus 2 is the number of sides so 18 + 2 = 20 sides --- a dodecagon

Answer 2

The sum of measure of the angles of an n-sided polygon is 180º(n-2)

3080/180 = 17.1111 so (n-2) must be greater than 17, so n must be greater than 19.

For a 20-gon, 180º(n-2) = 3240º; the "uncounted" angle would have to have measure of 3240º - 3080º = 140º . This is possible.

For a 21-gon, 180º(n-2) = 3420º; the "uncounted" angle would have to have measure of 3420º - 3080º = 340º. This is not possible for a convex polygon.

Therefore, the polygon must have 20 sides.