Question
Sat October 27, 2012 By: Ashrene

if the sum of all the angles of a convex polygon except one, is 2190 then the number of sides of the polygon must be?

Expert Reply
Sat October 27, 2012
Answer : Given :if the sum of all the angles of a convex polygon except one, is 2190
To find : the number of sides of the polygon
 
To compute for the total internal angles

180 * (n-2)

For a convex polygon, no angle should be greater than 180.

The total of internal angles should be more than 2190 but the difference should not be more than 180.

A convex polygon with 15 sides = 2340

(180 * (n -2)) - 2190 < 180
180 * (n-2) < 2370
n - 2 < 13.167
n < 15.167

The number of sides must be lest than 15.167 so the possible answers are 15, 14, ...

But also, the total internal angles should also be more than 2190.

Therefore Answer is 15 sides with a total of 2340 degrees total for internal angles.

2340 - 2190 = 150 degrees. (The angle not included, the other 14 internal angles sum up to 2190.)
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