In an isosceles triangle, the two base angles are equal, and the sum of all three angles in any triangle is always \(180\) degrees.
Let the measure of each base angle be \(x\). Since the vertex angle is \(110\) degrees, we can write the equation:
\[ x + x + 110 = 180 \]
Simplifying this gives:
\[ 2x + 110 = 180 \]
Now, subtract \(110\) from both sides:
\[ 2x = 70 \]
Next, divide both sides by \(2\):
\[ x = 35 \]
Thus, the measures of the base angles are \(35\) degrees each.
Therefore, the base angles of the triangle are \(35\) degrees.
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