Question 968945: 1) the sum of the measures of the interior angles of a convex n-gon is 2880. How many sides does it have?
2) how many sides does a polygon have if each of it's interior angle measures 108?
3) in a decagon, the sum of the measures of the first six interior angles is 1000. If the remaining angles are congruent, what is the measures of each?
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! 1) the sum of the measures of the interior angles of a convex n-gon is 2880. How many sides does it have?
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Equation:
(n-2)*180 = 2880
n-2 = 16
# of sides = n = 18
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2) how many sides does a polygon have if each of it's interior angle measures 108?
Each EXTERIOR angle is 180-108 = 72 degrees
The sum of ALL of the exterior angles = 360
# of sides = 360/72 = 5
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3) in a decagon, the sum of the measures of the first six interior angles is 1000. If the remaining angles are congruent, what is the measures of each?
Sum of All the interior angles = (10-2)180 = 8*180
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Sum of remaining angles = 8*180-1000 = 440 degrees
Ans: Each of the remaining angles = 440/2 = 220
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Cheers,
Stan H.
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