Step 1
Measure the shelf's depth, which is the distance it extends from the wall. For example, suppose that a shelf extends 12 inches from the wall.
Step 2
Hold a carpenter's level below the shelf perpendicular to the wall. The level's bubble will float to the center of its tube when it is horizontal. Depending on the shelf's angle, the level may make contact with the shelf's back or front.
Step 3
Measure the horizontal distance along the level between the wall and the front of the shelf. For example, suppose that this distance measures 11.5 inches.
Step 4
Divide the second measurement by the first. In the example, 11.5 divided by 12 is 0.958.
Step 5
Find the inverse cosine of this ratio on a scientific calculator. The inverse cosine of 0.958 is 16.66.
Step 6
Identify whether the level touched the front or back of the shelf in step 2. If the level touched the front of the shelf, the brace must be less than 90 degrees. Subtract 16.66 from 90, giving 73.33 degrees. If the level touched the back of the shelf, the brace must be more than 90 degrees. Add 16.66 to 90, giving 106.66 degrees.