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If XYZ is an isosceles triangle with base XZ , what is the measure of X? (picture below)

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It will be the same as angle y which is 180 - 86 = 94
If XZ is the base, wouldn't that mean that x and z have the same angles and y would have a different angle?

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Other answers:

You are right. I am not sure, but when I started doing the problem, I thought the student left out exactly what the base was and I guessed at what I thought he intended the base to be. Either I misread the problem initially or the problem was corrected after I posted my answer.
I have no idea either, I was just making sure
86/2 = to the base angles
therfore x=86/2 hope I am correct
In either case, the angle would be (with the problem as stated): (1/2)(180 - 94) = (1/2)(86) = 43. Yes, confirming @heedcom 's answer.
its 43
So @brianAC. what you want to do is determine what angle y is. And since we know angle x = angle z (by virtue of it being an isosceles triangle), you can set up an equation: x + y + z = 180 or, equivalently, y + 2x = 180 This will help you solve for x.

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