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We ban all bots. Embarrassed engineer dad here, trying to help daughter with some algebra. Ran into this problem which, to me, appears to have incomplete information. She was trying to solve it assuming that EF and ED are the same length and therefore everything can just be split in half and solved easily. But I redrew it to show that she could have the same angles given but have a very lopsided drawing as well.
I have a feeling we want to extend ED and EF out to that tangent line, but I tried that and just end up with more unknown angles.
I'm going to take a stab at it. See if you can follow my logic, and tell me if this is sound to you: Imagine a line CE. Of course if this figure isn't symmetrical, then there isn't enough information to solve this.
Since this is high school geometry I think it's safe to assume that it is. If you could prove that, then the bisecting strategy would work. This is an interesting question, I feel like there is a possible solution with the given info but it's certainly not obvious. I tried extending the line segments CD and CF out to the tangent line, but as you said, it just gives you more unknown angles. Adding and subtracting fractions Adding and subtracting mixed numbers The Language of Algebra Definitions The Language of Algebra Unit Quiz.
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