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Find the smallest positive equivalent of −40°.

Find the smallest positive equivalent of negative 40 degrees.

Let’s imagine that the directed angle negative 40 degrees is the angle between two rays 𝑂𝐴 and 𝑂𝐵, where 𝑂𝐴 is the initial side and 𝑂𝐵 is the terminal side of the angle. As our angle is negative, we will measure the angle between these two rays in a clockwise direction. This means that the 40-degree angle will be as shown in the diagram.

We need to find the smallest positive equivalent to negative 40 degrees. So we need to measure the same angle but in the other direction. A positive directed angle indicates we need to measure in a counterclockwise direction. We recall that angles at a point sum to 360 degrees. So, a positive equivalent of negative 40 degrees is found by subtracting 40 degrees from 360 degrees. Therefore, the smallest positive equivalent of negative 40 degrees is 320 degrees.

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