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An angle has a reference angle of 40° and its terminal side lies in Quadrant III. What are a possible positive measure and a negative measure for the angle?

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The positive measure is 220° and the negative measure is -140°.

How to find the measures of the angle?

First, we know that the reference angle is 40°, and it lies on the third quadrant.

So these 40° are measured from the negative x-axis (the axis where the quadrant starts).

This means that the angle measured in the standard way (from the positive x-axis) measures:

M = 40° + 90° + 90° = 220°.

To find the negative measure, we remember that any angle A is equivalent to:

B = A + n*360°.

Where n is an integer.

If we take n = -1 for our angle, we get:

M' = 220° + (-1)*360° = -140°.

So the positive measure is 220° and the negative measure is -140°.

If you want to learn more about angles:

https://brainly.com/question/16281260

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