In an isosceles triangle, the two base angles are equal. The sum of all the angles in a triangle is always 180 degrees.
Given that the vertex angle is 110 degrees, we can find the sum of the base angles:
\[ \text{Sum of the base angles} = 180^\circ - \text{vertex angle} = 180^\circ - 110^\circ = 70^\circ \]
Since the base angles are equal, we can divide the sum of the base angles by 2 to find each base angle:
\[ \text{Base angle} = \frac{70^\circ}{2} = 35^\circ \]
Therefore, the measures of the base angles are \(35^\circ\) and \(35^\circ\).
So the correct answer is 35 and 35 degrees.
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