SOLUTION: each interior angle of each regular polygon is twice the measurement of each exterior angle.how many diagonals does the polygon have?

Question 464025: each interior angle of each regular polygon is twice the measurement of each exterior angle.how many diagonals does the polygon have?
Answer by Gogonati(855) (Show Source): You can put this solution on YOUR website!
Let be x degree the measure of an exterior angle, then the measure of an interior
angle is 2x degree. Assume that the regular polygon has n sides (or angles).
We know that the sum of the interior angles is : and the sum
of exterior angles is: <=> , substituting this value
for x in the first equation we get: <=>
<=> <=>. Since the number of angles is
six, our regular polygon is a hexagon, and the number of diagonals drawn from one
vertex is three less then the number of sides, 6-3=3 diagonals.
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