Hello. My friends and I tried to solve this problem of this website.
http://www.gogeometry.com/problem/problem001.htm
But we could not. Can anyone please provide a proof of this problem? Thanks.
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Triangles ABC and BDC are similar (have equal angles). So, AC/BC=BC/DC. But AC=2*DC (from statement) and we obtain: BC^2=2DC^2 => BC=sqrt(2)*DC. Then, by law of sines for triangle BDC: BC/sin(135)=DC/sin(x), or sqrt(2)/sin(135) = 1/sin(x) and sin(x) = 1/2. Thus x = 30 degrees.
Thanks a lot :) Btw I don't know why but I cant vote on your comment!! It says you cannot vote twice. but the vote count isn't increasing!