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Question 285063: In a regular polygon,the measure of each angle is 174*
a)How many sides does the polygon have?
b)How many diagonals does it have?
c)What is the measure of an exterior angle?
d)What is the sum of the measure of the interior angles?
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! In a regular polygon,the measure of each angle is 174*
Note: Each exterior angle is the supplement of an interior angle.
So on your problem each exterior angle is 180-174 = 6 degrees
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a)How many sides does the polygon have?
Note: The sum of all of the exterior angles is 360 degrees.
Since 360/6 = 60, the polygon has 60 exterior angles; so the
polygon has 60 sides.
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b)How many diagonals does it have?
If it has 60 sides it has 60 vertices.
The number of lines determined by those 60 vertices is
60C2 = (60*59)/(1*2) = 1770
60 of those lines are sides of the polygon.
Therefore the polygon has 1770-60 = 1710 diagonals.
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c)What is the measure of an exterior angle?
6 degrees, as noted above
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d)What is the sum of the measure of the interior angles?
60*174 = 10440 degrees
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Cheers,
Stan H.
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