Answer:
The two angles are 597° and -483°
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°