Interesting. I got my upper bound of x < 70° in a completely different way, having to do with the fact that AD < BE. So I agree with your finding.
Running headlong down the trail of extrapolating information about the relative lengths of different line segments from known angles has yielded x < 65°, but I'm a lot less confident I didn't mess anything up here.
I haven't come up with anything which gives me a lower bound on x other than x > 0° yet. An insight on that could be heartening.
I also played with bisecting <ACB (or raising an altitude to intersect C). Unfortunately, it doesn't seem to generate anything I can use.
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ninetydegrees
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on 2007-12-14 02:10 am (UTC)Running headlong down the trail of extrapolating information about the relative lengths of different line segments from known angles has yielded x < 65°, but I'm a lot less confident I didn't mess anything up here.
I haven't come up with anything which gives me a lower bound on x other than x > 0° yet. An insight on that could be heartening.
I also played with bisecting <ACB (or raising an altitude to intersect C). Unfortunately, it doesn't seem to generate anything I can use.