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<div dir="ltr" data-setdir="false"><font size="3">Let's not overthink this one. The diagram could also be using non-Euclidian geometry. </font></div><div dir="ltr" data-setdir="false" style=""><font size="3"><br></font></div><div dir="ltr" data-setdir="false"><font size="3">But I'm thinking the problem is from a high school geometry test, so that it would not be correct to assume anything other than planar, Euclidian geometry, and not a projection of any kind. I missed the significance of the tick marks, which make it impossible for the "vertical" line to be in fact truly vertical. The angles are indeed 80-degrees and 100-degrees, making solving for the top angles trivial. I drew the scaled model to convince myself that this is a correct interpretation. </font></div><div dir="ltr" data-setdir="false" style=""><font size="3"><br></font></div><div dir="ltr" data-setdir="false" style=""><font size="3">-- Bob Primak</font></div><div dir="ltr" data-setdir="false" style="font-size: 13px;"><br></div><div style="font-size: 13px;"><br></div>
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On Saturday, February 21, 2026 at 06:51:05 PM EST, Jon Dreyer via LCTG <lctg@lists.toku.us> wrote:
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<p><font face="Times New Roman, Times, serif">Surely we can stretch
the problem in all sorts of ways: maybe it's not planar, maybe
apparently straight lines aren't straight, maybe it's on the
surface of a sphere, maybe the x is a Roman numeral 10, etc. But
there is a fairly standard language of geometry diagrams.
Typically, geometry diagrams are assumed planar unless we're
told otherwise, and lines that appear straight are assumed
straight unless we're told otherwise. But angles that look right
cannot be assumed to be right angles unless they have that
little right-angle-indicator square at the vertex.</font></p>
<p><font face="Times New Roman, Times, serif">So according to this
fairly standard interpretation, there's only one right answer.
Of course the problem is (probably intentionally) misleading
because the 80° angle does look closer to 90°.</font></p>
<p>- <br clear="none">
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Jon Dreyer<br clear="none">
<a shape="rect" href="http://www.passionatelycurious.com" rel="nofollow" target="_blank">Math Tutor/Computer
Science Tutor</a><br clear="none">
<a shape="rect" href="http://music.jondreyer.com" rel="nofollow" target="_blank">Jon Dreyer Music</a></p>
<div id="ydp818325a3yiv0207402348yqtfd89485" class="ydp818325a3yiv0207402348yqt7145883361"><div class="ydp818325a3yiv0207402348moz-cite-prefix">On 2/21/26 17:28, Richard Wagner via
LCTG wrote:<br clear="none">
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</blockquote></div></div><div id="ydp818325a3yiv0207402348yqtfd54275" class="ydp818325a3yiv0207402348yqt7145883361"><div><p>Just saw this emailed problem and accompanying thread, etc. I
am in Bob's corner to the extent that the problem is not simple.
Not enough information is given in the problem and assumptions
must be made where different assumptions can be correct!</p>
<p>Is the object planar or are we seeing a 3D projection of it. If
the latter, are we viewing it where one side is planar from our
vantage? If the right side is planar to us, then the answer is
30 degrees from the law of sum of angles in a triangle and the
angle at the bisection of the vertical line and horizontal line
<u>appears</u> to be 90 degrees. (From the Pythagorean Theorem
{a squared + b squared = c squared}, the ratio of the sides is
1:square root of 3:2 for opposite sides of a 30:60:90 degree
triangle. I'll never forget this ratio and formula from high
school <i>ad nauseam).</i> If we're seeing the left triangle as
a planar projection of a 3D object, the angle of the left
triangle at the vertical/horizontal bisection must be 80 degrees
for the given isosceles triangle. This leaves the angle on the
other side of this bisection open to question. Naively, one
would assume it to be 100 degrees, if one assumes the
"horizontal" line to be straight, and x to therefore be 20
degrees. However, one can't assume the bottom line to be
horizontal if the object is a projection, and from the
information given we can't determine angle at the
vertical/horizontal bisection for the triangle on the right side
of the projection.</p>
<p>Thus, I think the problem is unsolvable from the information
given, and I'm not surprised that AI is confused and gave
conflicting results. I agree with Olga: be cognizant to what AI
is doing and don't summarily assume it is giving correct answers
to your queries and conversations.</p>
<p>-Dick</p>
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