**Properties of a Parallelogram**

A parallelogram is a quadrilateral with opposite sides that are parallel and equal in length. It also has opposite angles that are equal. In a parallelogram ABCD, let angle A be 4/5 of angle B. To find angle A, we need to understand the properties of a parallelogram and use the given information to solve for the angle.

**Opposite Angles in a Parallelogram**

The opposite angles in a parallelogram are equal. Let's denote the measure of angle A as x and the measure of angle B as y. According to the given information, we know that angle A is 4/5 of angle B. This can be expressed as:

x = (4/5)y

**Sum of Interior Angles in a Parallelogram**

The sum of the interior angles in any quadrilateral is 360 degrees. In a parallelogram, opposite angles are equal, so we can say that:

x + y + x + y = 360

Simplifying this equation, we get:

2x + 2y = 360

Dividing both sides of the equation by 2, we have:

x + y = 180

**Solving for Angle A**

We have two equations:

x = (4/5)y
x + y = 180

To solve for angle A, we can substitute the value of x from the first equation into the second equation:

(4/5)y + y = 180

(9/5)y = 180

Multiplying both sides of the equation by 5/9, we get:

y = (5/9) * 180

Simplifying further, we have:

y = 100

Now, we can substitute this value of y into the first equation to find the value of x:

x = (4/5) * 100

x = 80

Therefore, angle A is 80 degrees.

**Conclusion**

In a parallelogram ABCD, if angle A is 4/5 of angle B, we can determine the measure of angle A by using the properties of a parallelogram. By setting up equations based on the given information and the sum of interior angles in a parallelogram, we can solve for the measures of angles A and B. In this case, angle A is found to be 80 degrees.