Do the diagonals from a corner of a regular polygon always make equal angles?

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).

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