Are all the angles at the point B inside this regular heptagon the same? What if I was to construct diagonals in any regular polygon, would they always be the same?

This was a problem posed on page 30 in Paul Lockhart’s book, “Measurement” which made me think for a few hours. I’ve posted my argument below and would be really interested to see if anyone would do this in a different way(Here is a link to the first geogebra file used in the video if you’re interested).

@mrbartonmaths Genuinely all of them - can't think of one that I haven't enjoyed or learnt something from. 1 month ago

Flippin eck!Just listened to 8 hours of @mrbartonmaths maths podcasts. Absolutely brilliant-so much to reflect upon.Thanks Craig! #longdrive1 month ago

@GWAS A tiny bit emotional finishing off this speech for our first ever graduating class... 2 months ago