Given:
- Rectangle ABCD
- Diagonals of the rectangle intersect at point O
- Angle COD = 78 degrees

To find:
- Angle OAB

Explanation:

Properties of Rectangles:
1. Opposite sides of a rectangle are parallel.
2. Opposite sides of a rectangle are equal in length.
3. Diagonals of a rectangle are equal in length.
4. Diagonals of a rectangle bisect each other.

Identifying Angles in the Rectangle:
Let's label the angles in the rectangle ABCD as follows:
- Angle A = Angle C (opposite angles)
- Angle B = Angle D (opposite angles)
- Angle OAB = Angle OBC (alternate angles)
- Angle OBA = Angle ODC (alternate angles)

Using Properties of Rectangles:
Since ABCD is a rectangle, we know that:
- Angle A + Angle B + Angle C + Angle D = 360 degrees (sum of angles in a rectangle)
- Angle A + Angle C = Angle B + Angle D (opposite angles are equal)

Finding Angle ODC:
From the given information:
- Angle COD = 78 degrees

Since diagonals of a rectangle bisect each other, we know that:
- Angle ODC = Angle OCD = 78/2 = 39 degrees

Finding Angle OAB:
Using the property of opposite angles being equal:
- Angle A + Angle C = Angle B + Angle D

Substituting the known values:
- Angle A + 39 degrees = 90 degrees + 39 degrees (since a rectangle has 90-degree angles)

Simplifying the equation:
- Angle A = 90 degrees (canceling out the common term 39 degrees)

Therefore, in rectangle ABCD, Angle OAB is equal to 90 degrees.

Final Answer:
Angle OAB = 90 degrees.

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