Help me with this geometry problem, please?

Question

Will you help me with this geometry question, please?
Thank you a bunch.

What is the lowest value of n for which an n-gon has interior angles of non-integer degree measure?

Thanks a bunch. <3

..and show how to get to the result, please? :/ Thank you.

Answer 1

The exterior angles of a n-gon add up to 360.

n = 7
360/7 ~ 51.4

The interior angles will be 180 - 51.4 ~ 128.6

Answer 2

We know that the sum of exterior angles of a polygon is always 360 degrees,and that an interior angle of a polygon is always 180 degrees-exterior angle
Hence an interior angle to be of non=integer,the exterior angle should also be non-integer.
360 divided by 3,4,5and 6 gives quotient of 12o,90,72 and 60 ,all of which are integers
we get an non-integer quotient only when the sides of the polygon is 7 because 360/7=51.4
the exterior angle being non-integer,the interior angle would also become a non-integer i.e.180-51.4=128.6 degrees
Hence a regular polygon with minimum 7 sides will have a non-integer degree measure of interior angles

Answer 3

A 7-gon, also known as a heptagon, as interior angles of 128.6º. I am assuming you mean a regular n-gon, so that all interior angles are the same measure.

Answer 4

Hey there!

7. Here's why.

3-sided polygon=60 degrees.
4-sided polygon=90 degrees.
5-sided polygon=108 degrees.
6-sided polygon=120 degrees
7-sided polygon=128.6 degrees.

So it is 7. The proof is by using the formula 180(n-2)/n, where n is the number of sides. This formula is to find the measure of each interior angle in a regular polygon.

Hope it helps!

Answer 5

Since the exterior angles always add up to 360, find the lowest number that does not go into 360 evenly. Shouldn't take long.

Answer 6

oh man. u r screwed...thnks anyways for the two pts.