Final answer:
The highest degree measure possible for an angle in an isosceles triangle is just below 180 degrees, because a triangle's angles must sum to 180 degrees and no single angle can reach or exceed 180 degrees by itself.
Step-by-step explanation:
The highest degree measure possible for an angle in an isosceles triangle is just below 180 degrees. Remember, a triangle, by definition, is a three sided figure lying on a plane with the sum of its interior angles always adding up to 180 degrees.
In the case of an isosceles triangle, which has two sides of equal length, the angles opposite these two sides are also equal. The third angle, which could potentially be the largest, is what the question is asking for.
So if the two equal angles are very small, the third angle can be very large. However, if the two equal angles were to shrink to 0 degrees, which isn't possible in a real triangle, only then would the third angle approach 180 degrees.
In reality, the third angle can be very close to, but never exactly, 180 degrees for the figure to remain a triangle.