SOLUTION: a regular polygon of n-sides is such that each interior angle is 120 degree greatet than the exterior angles. find 1. the value of n 2. the sum of all the interior angled.

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Question 1063188: a regular polygon of n-sides is such that each interior angle is 120 degree greatet than the exterior angles. find
1. the value of n
2. the sum of all the interior angled.
Found 2 solutions by Boreal, ikleyn:
Answer by Boreal(15235)   (Show Source): You can put this solution on YOUR website!
The exterior angles are x
The interior angles are x+120
the two add to 180 degrees.
Therefore, 2x+120=180
2x=60
x=30 degrees exterior angles
all of the exterior angles (n) add to 360 degrees,
Therefore, 360/30=12 sides
(n-2)*180 is their sum or 1800
150 degrees is an interior angle, and 12 of them add to 1800 degrees.
Answer by ikleyn(52797)   (Show Source): You can put this solution on YOUR website!
.
a regular polygon of n-sides is such that each interior angle is 120 degree greater than the exterior angles. find
1. the value of n
2. the sum of all the interior angled.
~~~~~~~~~~~~~~~~~~~~~~~~~~ 

A + B = 180,
A - B = 120

=====> A = 150 degs (interior angle);  B = 30 degs (exterior angle).

====>  n =  = 12.


The sum of all interior angle of a polygon is 360 degs always (in all regular cases).


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