Help with Finding Angles of an Octagon

[tomtomtom1]

Hi all

I was wondering if someone could help with the following:-

I have a regular octagon.

Find angle CBA, ACB, BAC.

Lines BA and AC are equal in length.


I have done the following:-

Found all the internal angles and all the external angles.

I know that I have an isosceles triangle because BA & AC are equal so the base angles are equal.

My guys felling is that I need to divide 135 by 2 to get 67.5, so my base angles ate 67.5, 67.5 and my third angle is 45.

But I cannot explain why I dividing 153 by 2 gives the correct answer can anyone explain?

 

[verty]

For me, the easiest way to do this is to start with angle $\hat{A}$, you should be able to find it without knowing any other angles. Hint: extend AC and BC past A.