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

Answer 1

Let's call the shorter side of the rectangle "x" and the longer side "y". Since the angle formed by the diagonal and one side of the rectangle is 36°, we can conclude that the angle formed by the diagonal and the other side of the rectangle is also 36°.

Let's draw a diagram to better understand the situation:

y
-------------
| |
| |
x |_______| 36°

Since we have a rectangle, the opposite angles are equal. So, we have:

y
---------- --------
| |
| 36°
36° |
---------- x

Now, let's calculate the angle between the diagonals using the formula for angles in rectangles. Angle ABC (opposite the shorter side and between the diagonals) is equal to 180° - 36° - 36° = 180° - 72° = 108°.

Therefore, the measure of the angle that lies opposite the shorter side and is between the diagonals is 108°.