Catriona Shearer's "Tilted Twin" puzzle

I just stumbled across Ben Orlin's "Math With Bad Drawings" blog, where he mentions Catriona Shearer's geometry puzzle tweets.  Both Orlin's blog and Shearer's tweeted puzzles are enormous fun.  Here is the answer to the puzzle above:

 cos(?) = 1/2 ; ? = 60 degrees.  The answer was tweeted at the author by Alaadin Cizer.