By connecting every other vertex of a regular pentagon, you form a symmetrical star. How and why is the sum of the star's angles congruent to that of any other non-regular pentagon's star?

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bobbinhood

Just a guess: The sum of the measures of the interior angles of any pentagon is always 540 degrees. It doens't matter whether that pentagon is regular or not, it will always add up to 540 degrees, just like the sum of the measures of the interior angles of every triangle is always 180 degrees. Since the interior angles of pentagons always sum to 540 degrees, it makes sense that the angles formed from connecting the points would also always sum to the same thing (whatever that amount is).

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