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In the figure above, $\overline{A E} \| \overline{C D}$ and segment $A D$ intersects segment $C E$ at $B .$ What is the length ofsegment $C E ?$

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So for this one, the first thing we have to realize is that this angle and that angle or the same because their opposite angles. And so let me to straka situation. So if we had this England this angle, we know it's the same because this entire thing adds to one eighties. Let's just call this and accent that Why So experts wise people to one eighty? Well, this is also a straight line right here. So we know why. Plus something as he would want eighties that's clearly X. So clearly those things are the opposite angles, which are the same. So then we also have to realize that this angle A and this angle t are the same as well, because if we take that and dry like this, where this line represents eighty, I just expend it, expended it a little bit out farther, and then this is going to be seedy. This is going to be a so a T men. This is eighty right here. So then we know that this England the singular the same by the same principle that I should right here this England, the single are also the same by the same principle, Aisha. But here. So then, that means that angle A in England TV are also the same because that this right here and this right here tenseness in this. So then if two angles are the same, that the third angle must automatically be the same in a triangle because there's three angles. So then this and this are actually going to be similar triangles. So then, if we Richard tried her, draw it out where, fortunately, you know that it's going to be like this. Where? This triangle right here. What a is the same Misty's I'm gonna call that D. C is the same as angle. Cease that C. Then this one must be bi So then we know that b g, which is right here, is going to be five. I'm just moving this five over here just to draw it out next to each other to see which one are you professional? Well, if this is turning, this is five we clearly got from B D to a B by multiplying it by two. So then we have to take whatever BC is and multiply by two to get eight. That's just gonna be for this four times two is eight. So then, if we know that BC is going to be four, that's twenty four, and we're looking for this entire Les of C. We just have to add the two components that make up see. So if we do four plus eight, that becomes twelve. So we know twelve is our answer.

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