Question 480043
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There is no isosceles right triangle with a base angle that measures 60 degrees.  In an isosceles right triangle, the vertex angle is 90 degrees and each base angle is 45 degrees.<br>
In an isosceles triangle with one base angle 60 degrees, the other base angle is 60 degrees, so the sum of the two base angles is 120 degrees.  Then, since the sum of the angles of a triangle is 180 degrees, the measure of the vertex angle is 180-120 = 60 degrees.  So if the statement of the problem was supposed to state "isosceles triangle" instead of "isosceles right triangle", the answer is that the vertex angle is 60 degrees.<br>
But as the problem is posted, with an "isosceles right triangle", the problem is faulty and has no solution.<br>