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<p>I assumed the tick marks indicate that the two lines, for the
left triangle, are identical in length resulting in an isosceles
triangle. If so, and assuming the presented diagram is planar, the
bisection of the vertical line with the horizontal line does not
yield 90 degree angles for the two inner triangles, which is the
way they appeared to me as I looked at the figure (and it also
appeared to me that the horizontal line was straight). From the
isosceles triangle perspective😉, x = 20 degrees. From the 90
degree angle perspective, x = 30 degrees. Both answers were given
as possible options. To me, the primary assumption that must be
made is to assess the angle(s) at the vertical/horizontal
intersection.</p>
<p>I still don't think enough information was given in the problem
to establish a clear conclusion for this assumption. Thus, I
maintain the problem is faulty.</p>
<p>Probably not worth further contemplation as we encounter the
approaching blizzard. I can't wait!😇</p>
<p>-Dick </p>
<div class="moz-cite-prefix">On 2/22/2026 3:00 AM, Robert Primak via
LCTG wrote:<br>
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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>
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<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>
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<div dir="ltr" data-setdir="false" style=""><font size="3">--
Bob Primak</font></div>
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<div> On Saturday, February 21, 2026 at 06:51:05 PM EST, Jon
Dreyer via LCTG <a class="moz-txt-link-rfc2396E" href="mailto:lctg@lists.toku.us"><lctg@lists.toku.us></a> wrote: </div>
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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">
</p>
<p style="font-family:Times, serif;"> Jon Dreyer<br
clear="none">
<a shape="rect"
href="http://www.passionatelycurious.com"
rel="nofollow" target="_blank"
moz-do-not-send="true">Math Tutor/Computer Science
Tutor</a><br clear="none">
<a shape="rect" href="http://music.jondreyer.com"
rel="nofollow" target="_blank"
moz-do-not-send="true">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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<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>Â 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>
<div class="ydp818325a3yiv0207402348moz-signature">-</div>
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