In an isosceles triangle, the vertex angle is the angle opposite the base, and the two base angles are equal. To find the measures of the base angles, we can use the property that the sum of the angles in a triangle is always 180 degrees.
Given that the vertex angle is 110 degrees, we can find the measure of the base angles as follows:
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Subtract the vertex angle from 180 degrees: \[ 180^\circ - 110^\circ = 70^\circ \]
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Since the two base angles are equal, we divide this result by 2: \[ \frac{70^\circ}{2} = 35^\circ \]
Thus, the measures of the base angles are both 35 degrees.
So the answer is 35 and 35 degrees.
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