Question 1191938: How many sides does a polygon have if the sum of its interior angles is 7 times the sum of its exterior angles? Found 2 solutions by Theo, greenestamps:Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website! sum of interior angles = (n-2)*180
sum of exterior angles is always 360.
7*360 = (n-2)*180
divide both sides of this equation by 180 to get
7*2 = n-2
add 2 to both sides of this equation and simplify to get:
16 = n
number of sides is equal to 16.
sum of exterior angle is 360.
sum of interior angles is 14*180 = 2520
2520/360 = 7
The way the problem is stated, the result has to be independent of what type of polygon it is, so we can choose the special case where the polygon is regular.
Then, if the sum of the interior angles is 7 times the sum of the exterior angles, then the measure of one interior angle is 7 times the measure of one exterior angle.
x = exterior angle
7x = interior angle
The sum of the measures of an interior angle and an exterior angle is 180 degrees:
x+7x=180
8x=180
x=180/8=22.5
The measure of an exterior angle of a regular polygon is 360 degrees, divided by the number of sides.
