SOLUTION: In paragraph form, prove that there is no regular polygon with
each interior angle measuring 145°
(Prove using indirect proof as well)
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-> SOLUTION: In paragraph form, prove that there is no regular polygon with
each interior angle measuring 145°
(Prove using indirect proof as well)
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Question 1106736: In paragraph form, prove that there is no regular polygon with
each interior angle measuring 145°
(Prove using indirect proof as well) Answer by Edwin McCravy(20064) (Show Source):
The formula for the common measure of each of the
interior angles of a regular polygon with n-sides
is 145°.
We set that equal to 145°:
Multiply both sides by n
Add 360° to both sides:
Subtract 145°n to both sides
Divide both sides by 35°
Cancel the degrees:
A regular polygon can only have a integer
for its number of sides.
Proved!
------------------------
Indirect proof:
Assume that there is a regular polygon such that each of
its interior angles of a regular polygon with n-sides is.
The formula for the common measure of each of the
interior angles of a regular polygon with n-sides
is 145°.
We set that equal to 145°:
Multiply both sides by n
Add 360° to both sides:
Subtract 145°n to both sides
Divide both sides by 35°
Cancel the degrees:
n is not an integer, so there is no such regular
polygon. This contradicts the assumption that
there is such a regular polygon.
Proved!
Edwin
