<PRE><B>Question 285063</B>
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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