2. What is a positive coterminal angle to -123° that is between 500° and 750° and a negative coterminal angle to -123° that is between −300° and −500°?

The two angles are  597° and -483°

Step-by-step explanation:

A coterminal angle to a random angle A, is an angle that has the same terminal side as A.

If we know the angle A, all the coterminal angles to A can be written as:

A + n*360°

Where n is an integer number.

In this case, we know that:

A = -123°

And we want to find a coterminal angle that is between 500° and 750°

Then we can do:

X = -123° + n*360°

And find the value of n such that X is between the desired values.

if we use n = 1 we get:

X = -123° + 1*360° = 237°

This is not enough, we can discard it.

If we use n = 2, we get:

X = -123° + 2*360° = 597°

This is a coterminal angle to -123°, and is in between 500° and 750°.

Now we want to find a coterminal angle to -123° that is in between -300° and -500°, we can do the same thing as before, but now we can try with negative values of n.

We can start with n = -1, then:

X = -123° - 1*360° = -483°

This is a coterminal angle to -123°, and is in between -300° and -500°.

Then the two angles are:

597° and -483°

look a the sides they are perpendicular