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.
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°.