Parallelogram ABCD: Angle A = 80 degrees

To find the measure of angle C in parallelogram ABCD, we can use the properties of parallelograms and the fact that opposite angles in a parallelogram are congruent.

Properties of parallelograms:
1. Opposite sides of a parallelogram are parallel.
2. Opposite sides of a parallelogram are congruent.
3. Opposite angles of a parallelogram are congruent.
4. Consecutive angles of a parallelogram are supplementary (add up to 180 degrees).

Since ABCD is a parallelogram, we know that angle A and angle C are opposite angles, meaning they are congruent. Therefore, if angle A is 80 degrees, angle C is also 80 degrees.

Proof:
1. Given: ABCD is a parallelogram.
2. By definition of a parallelogram, opposite angles are congruent.
3. Therefore, angle A and angle C are congruent.
4. Given: Angle A = 80 degrees.
5. Therefore, angle C = 80 degrees.

Visual representation:

```
A _________ B
| |
| |
| |
|_________|
D C
```

In the parallelogram ABCD, angle A and angle C are opposite angles. Since angle A is given as 80 degrees, angle C must also be 80 degrees by the properties of parallelograms.

Conclusion:
In parallelogram ABCD, if angle A is 80 degrees, then angle C is also 80 degrees.

ABCD is a parallelogram where A=80.

So, to find angle C
180 - 80 = 100 (because adjacent angles are supplementary)

Angle C = 100•