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

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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) About Me  (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 :n%2A2x=%28n-2%29%2A180 and the sum
of exterior angles is:n%2Ax=360 <=> x=360%2Fn, substituting this value
for x in the first equation we get:n%2A2%2A360%2Fn=%28n-2%29%2A180 <=>
4%2A180=%28n-2%29%2A180<=>4=n-2 <=>n=6. 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.