Geometric Solution to The 15o Problem


    Recall, that we will be working with a square ABDE.



    Now let's choose a point C so that the triangle CDE is isosceles with angles 15o at D and E.



    We want to find out what type of triangle ABC is.



    To begin, choose a point F inside the triangle such that triangle BFD is congruent to triangle DCE.



    Notice that BF is perpendicular to CD of the equilateral triangle CDF.



    By the previous statement, BC = BD = AB.

    Therefore, we can conclude that triangle ABC is equilateral.


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