SOLUTION: In paragraph form, prove that there is no regular polygon with each interior angle measuring 145� (Prove using indirect proof as well)

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): You can put this solution on YOUR website!

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

RELATED QUESTIONS
I really need help with 2 proofs i would love if someone helped me. thanks!... (answered by Edwin McCravy,ikleyn)

Starting from the sum of exterior angles prove that in a regular polygon of n sides, the... (answered by solver91311)

Prove this using indirect proof in two-column form. Given: 𝑀𝑃 ⊥ ̅NO Prove:... (answered by MathLover1)

name the regular polygon in which each exterior angle is congruent with each interior... (answered by ikleyn)

Write a proof using indirect proof in paragraph form. Given: Transversal 𝑡 cuts lines (answered by greenestamps)

Prove this using direct proof in paragraph form. Given: 𝑀 is the midpoint of 𝑋𝑌 (answered by MathLover1)

Is it possible to have a regular polygon where each interior angle is equal to 145? If... (answered by Alan3354)

Prove that the exterior angle of a regular decagon is one - third the interior angle of a (answered by Theo)

how many sides are there for a regular polygon whose each interior angle is 108... (answered by Alan3354,ikleyn)