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@urodacus how to find X?

How do you find the angle inside a kite?

I found this problem in my geometry textbook and I’ve been staring at the picture for a while and I am out of ideas. [image] According to the official answers sheet the answer is 15 degrees given in sexagesimal units. The rules for this is that you may not use trigonometry or triangle similarity. So in essence is a puzzle. Well, i am not good with constructions. Does any of you guys can help me? You can use isosceles triangles, circles, equilateral triangles, congruence and all of those sort…