MethodMath
Sarah Mitchell
May 10, 2026

Can you solve this triangle puzzle where the answer is not what it seems viral geometry problem

I found this geometry problem on Twitter and nobody in my class can solve it:

In triangle ABCABC, angle A=50A = 50^\circ, angle B=60B = 60^\circ, angle C=70C = 70^\circ.

Point DD lies on ABAB such that DCB=30\angle DCB = 30^\circ.
Point EE lies on ACAC such that EBC=20\angle EBC = 20^\circ.

Find DEB\angle DEB.

I tried using the sum of angles in triangles and got multiple possible answers. One person said 3030^\circ, another said 4040^\circ.

I think this requires constructing an equilateral triangle somewhere or using the law of sines. Can someone solve this with a clear geometric construction approach?

Also the answer is apparently 3030^\circ but I dont see how.

1 answers1.1k views
4 comments
Sarah Mitchell
Sarah MitchellMay 11, 2026

I keep trying to solve this and getting different answers each time

Alex Kim
Alex KimMay 11, 2026

the trick is constructing an equilateral triangle on AB. then you get congruent triangles that reveal the missing angle.

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1 Answer

James O'Neill
James O'NeillMay 26, 2026
For geometry problems, I would start by marking the invariant: equal lengths, equal angles, parallel lines, or a conserved area. For a circle, the two formulas that connect most computations are $$C=2\pi r,\qquad A=\pi r^2.$$ One intuitive derivation of the area formula is to add thin circular rings. A ring at radius $t$ has approximate circumference $2\pi t$, so $$A=\int_0^r 2\pi t\,dt=\pi r^2.$$ If the problem is about angles, drawing an auxiliary parallel line often turns the question into alternate interior angles.
1 comment
Liam Henderson
Liam HendersonMay 27, 2026

Could you add one more line on the condition where this method fails?

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