Geometry Question (1 Viewer)

[GaDaMIt]

Find the number of sides of a regular polygon if each interior angle is 172'

How do you do a question like that? From common sense ive figured you can do it by

180(n-2) = n x angle

So that would be 180n - 360 = 172n

8n = 360

so n = 45

One of my friends said the following for this specific example..

180-172
=8
360 divided by 8
= number of sides

but she cant explain why that is done to me.. her tutor just taught her and she remmebered..

my cazin also did some weird thing about 360/n + 2 theta = 180.. i dunno..

So uhh.. whats the proper way you would approach this question in a test situation?

 

[onebytwo]

i think your way is the most logical.
your friends method is also correct, but doesnt seem to illustrate proper reasoning

 

[SoulSearcher]

I would go with your method, as it is easy to understand.

 

[Templar]

Both methods are logical, just that the second one requires a bit more explanation.

180(n-2)=@n
180n-360=@n
180n-@n=360
(180-@)=360/n
so n=360/(180-@)

 

[Sober]

The second one makes alot of sense conceptually as well. When you take 180-172 = 8 you get how much the edge deviates from contuing in a straght line, and since to make a complete revolution it needs to deviate 360 degrees it will happen 360/8 times.

 

[airie]

Your friend's method comes directly from the theorem that the sum of all exterior angles of a regular polygon is always equal to 360 degrees.