Parallelogram ABCD:
Given that we have a parallelogram ABCD and the measure of angle D is 110 degrees. We need to find the measures of angles A and B.

Properties of a Parallelogram:
To find the measures of angles A and B, we can make use of the properties of a parallelogram:

1. Opposite angles of a parallelogram are equal.
2. Adjacent angles of a parallelogram are supplementary (i.e., they add up to 180 degrees).

Angle A:
Since opposite angles of a parallelogram are equal, angle A is equal to angle C. We can use this information to find the measure of angle A.

1. We know that the sum of angles in a triangle is 180 degrees.
2. In triangle ADC, angle A + angle C + angle D = 180 degrees.
3. Substituting the given values, we have angle A + angle A + 110 degrees = 180 degrees.
4. Simplifying the equation, we get 2 * angle A = 70 degrees.
5. Dividing both sides by 2, we find that angle A = 35 degrees.

Therefore, angle A in parallelogram ABCD measures 35 degrees.

Angle B:
Since adjacent angles of a parallelogram are supplementary, angle B is supplementary to angle A (and angle C is supplementary to angle D).

1. We know that supplementary angles add up to 180 degrees.
2. Therefore, angle A + angle B = 180 degrees.
3. Substituting the value of angle A from the previous calculation, we have 35 degrees + angle B = 180 degrees.
4. Solving for angle B, we find that angle B = 180 degrees - 35 degrees.
5. Simplifying the equation, we get angle B = 145 degrees.

Therefore, angle B in parallelogram ABCD measures 145 degrees.

Summary:
In parallelogram ABCD, angle A measures 35 degrees and angle B measures 145 degrees. These measurements are obtained by applying the properties of a parallelogram, such as the equality of opposite angles and the supplementary nature of adjacent angles.