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This is a systems problem.
They give you a couple of pieces of information to construct your system of equations.
First they tell you that the third angle (which I will call B) is 1/7 as large as each of the two base angles. Lets construct the first equation.
(B is the third angle, A is the measure of the base angles.)
We know that triangles sum up to 180 degrees, which gives us our second equation, making our system look like this:
Use the solved equation and put it into the second one.
You want to group your A's together, so you must get a common denominator.
Divide by (15/7), which is multiplying by (7/15).
Now that you have a numerical value for A, use it in the simplest equation to find the numerical value of the other variable.
The solution, then, is A=84 and B=12.
Remember, isosceles means that two of the angles are the same measure.