The Student Room Group
Competition - post a photo you've taken of nature >>
Competition - post a photo you've taken of nature >>
Competition - post a photo you've taken of nature >>

Maths question from Cambridge natural sciences past paper

I really don't know where to start with this question to be honest.
NSAA 2016 Q14.png42.7KB
Original post by knoxode
I really don't know where to start with this question to be honest.


Starting point is going to depend on what you know. So, first off, what do you know about the angles in a regular polygon?
Reply 2
Avatar for knoxode
knoxode
OP
12
Original post by ghostwalker
Starting point is going to depend on what you know. So, first off, what do you know about the angles in a regular polygon?


The interior angle of a regular polygon is equal to the sum of the interior angles, divided by the number of sides.
Original post by knoxode
The interior angle of a regular polygon is equal to the sum of the interior angles, divided by the number of sides.


OK. Can't usefully use that.

So, most direct root, IMO, is to look at the exterior angle.

If we follow the line of the polygon round, it goes through a full 360 degrees, and this is n lots of the exterior angle, one after the other.

Hence the exterior angle equals 360/n, and that will be an angle in the isosceles triangle. Can you take it from there?
Reply 4
Avatar for knoxode
knoxode
OP
12
Original post by ghostwalker
OK. Can't usefully use that.

So, most direct root, IMO, is to look at the exterior angle.

If we follow the line of the polygon round, it goes through a full 360 degrees, and this is n lots of the exterior angle, one after the other.

Hence the exterior angle equals 360/n, and that will be an angle in the isosceles triangle. Can you take it from there?


So perhaps the other to angles in the isosceles triangles (that are not x) will be equal to n/360 - 180?
Original post by knoxode
So perhaps the other to angles in the isosceles triangles (that are not x) will be equal to n/360 - 180?


Not sure how you get that.

Each of the not-x angles is 360/n, since one is an exterior angle and it's isosceles.

Hence for the whole triangle:

x + (360/n) +(360/n) = 180

And rearrange.
(edited 6 years ago)

Quick Reply

Related discussions

Latest

Trending

Trending

Articles for you