Hello mmsThis is surprisingly tricky. The answer is , which I can prove using trigonometry, but I'm not sure whether there's a simpler explanation. My solution is this.
Let the points on the lines and be and respectively, and suppose that .
Then (isosceles )
and
So using Sine Rule on ’s and :
Now use Cosine Rule on :
Perhaps someone can come up with a more direct method?
Grandad
PS Correction!
Sorry, I calculated the wrong angle. It's that's . bjhopper is quite right.
your diagram is a bit distorted..the line forming the x angle should be oblique.this is not an easy problem.in fact it is more of a puzzle.it comes uo on the internet as the hardest / easiest problem in geometry.
the answer is 30.proof requires construction lines sorry i cannot put drawings in this reply.other responders migth help
bjh