I don't understand what the question means.....

In a rectangle, a diagonal forms a 36° angle with a side. Find the measure of the angle between the diagonals, which lies opposite the shorter side.

The diagonal forms a 54° angle with the short side.

Now you have an isosceles triangle with two 54° angles and a third angle, which is the one you want...

ANSWER:72 degrees

To find the measure of the angle between the diagonals in a rectangle, let's start by drawing a rectangle and labeling the given angles.

First, draw a rectangle with four sides. Label one of the shorter sides as "a" and label the longer side as "b".

Next, draw a diagonal that forms a 36° angle with side "a". Label this diagonal as "d1".

Now, we need to find the angle opposite the side "a". Since we know that the sum of angles in a rectangle is 360°, we can calculate the missing angles in the rectangle.

In a rectangle, opposite angles are equal. So, the angle opposite side "a" is also 36°. Let's label this angle as "x".

Next, draw the other diagonal of the rectangle. Label this diagonal as "d2".

The angle between the two diagonals is opposite to side "a". Since the opposite angles are equal in a rectangle, the angle between the diagonals is also "x" degrees, which is 36°.

Therefore, the measure of the angle between the diagonals, which lies opposite the shorter side, is 36°.

To understand the question, let's first visualize the situation. We have a rectangle, which is a quadrilateral with four right angles.

Now, let's define the terms mentioned in the question.
- "Diagonal" refers to a line segment connecting two non-adjacent vertices of the rectangle.
- "Angle with a side" means that one of the diagonals forms a 36° angle with one of the sides of the rectangle.
- "Angle between the diagonals" refers to the angle formed by the two diagonals at their intersection point. This angle is opposite the shorter side of the rectangle.

To find the measure of the angle between the diagonals, we need to establish a relationship between the given angle (36°) and the desired angle.

Let's label the rectangle's vertices as A, B, C, and D, starting from the top left and moving clockwise. Suppose the shorter side of the rectangle is AB, and the diagonal forming a 36° angle with AB is AC. Thus, the diagonal opposite AB will be BD.

To find the measure of the angle between the diagonals, we can use the fact that the sum of the angles in a quadrilateral is 360°. In this case, we can consider quadrilateral ABCD formed by the two diagonals.

1. We know one angle of the quadrilateral: ∠ACB = 36°.
2. We also know that the quadrilateral is a rectangle, so the opposite angles are congruent: ∠BCD = ∠ACB = 36°.
3. Using the fact that the sum of angles in a quadrilateral is 360°, we can express the measure of the angle between the diagonals: ∠ABD = 360° - ∠ACB - ∠BCD.

Therefore, to find the measure of the angle between the diagonals, substitute the given values into the equation:
∠ABD = 360° - 36° - 36°.

Simplifying the equation, we have:
∠ABD = 360° - 72°.

Calculating the result, we find:
∠ABD = 288°.

Thus, the measure of the angle between the diagonals, which lies opposite the shorter side, is 288°.