# 4 equations, 4 variables. Why can't I solve it?

**URL:** <https://boards.straightdope.com/t/4-equations-4-variables-why-cant-i-solve-it/1018582>\
**Category:** Factual Questions\
**Tags:** science-math\
**Created:** [May 20, 2025, 1:19pm UTC](https://boards.straightdope.com/t/4-equations-4-variables-why-cant-i-solve-it/1018582 "2025-05-20T13:19:10Z")\
**Posts on this page:** 1\
**Page:** 4

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**Author:** ![DPRK](https://avatars.discourse-cdn.com/v4/letter/d/4491bb/32.png) [@DPRK](https://boards.straightdope.com/u/DPRK)\
**Post date:** [May 26, 2025, 10:05am UTC](https://boards.straightdope.com/t/4-equations-4-variables-why-cant-i-solve-it/1018582/61 "2025-05-26T10:05:45Z")

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> [@Dr.Strangelove](#):
>
> (I did try using @Stranger_On_A_Train 's suggestion of using the isosceles property, but I didn’t get anywhere).

Just the constraints about the various triangles being isosceles are not enough to determine everything. However, that plus, e.g., the 30-degree angle should be enough. For example, reflect the point X/Y through the bottom side and add the resulting equilateral triangle to the sketch. Now you can see enough isosceles triangles to chase the 20-degree angle and see that X + 20 = 60.

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