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Inside a square ABDE, take a point C so that CDE is an isosceles triangle with angles 15 degrees at D and E. What kind of triangle is ABC?

I put C close to the bottom to get my isosceles triangle. According to the answer in back, the triangle ABC is equilateral. The hint that went along with the answer is pick a point F to make a triangle congruent to triangle CDE. Are there theorems that I am missing to see how this could work out? I've spent a while on this and I feel like I'm missing something obvious.

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# College Euclidean Geometry

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