It's similar to how you would do the question for the first eight parts, except that the angle is composed of two parts.

All angles I am typing here are assumed to be in degrees.

0 < x < 360 implies that
0 < 2x < 720 and
-60 < 2x - 60 < 660

Essentially, we are looking for all possible angles of 2x - 60 which spans two complete cycles of angles from -60 to 660 so that the resulting transformation/manipulation from 2x - 60 to angle x will net us all angles of x between 0 and 360.

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tan (2x - 60) = -1 / sqrt 3

Basic angle, alpha = positive inverse tangent (1 / sqrt 3)
Basic angle, alpha = 30

Since tan (2x - 60) has a negative value, 2x - 60 lies in the second or fourth quadrant.

Be careful here as the angle range -60 to 0 is also a fourth quadrant angle. A hidden angle might appear there.

2x - 60 = angles in second or fourth quadrant

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2x - 60 can take one of these values (we reject them later if necessary)

1. Fourth quadrant, previous cycle
2. Second quadrant
3. Fourth quadrant
4. Second quadrant, next cycle
5. Fourth quadrant, next cycle

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The angles for 2x - 60 are

1. -alpha = -30 (this is why we have to be careful as I mentioned earlier; an angle does exist here after all)
2. 180 - alpha = 150
3. 360 - alpha = 330
4. 540 - alpha = 510
5. 720 - alpha = 690 (rejected, since it is out of range of -60 to 660)

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2x - 60 = -30, 150, 330, 510
2x = 30, 210, 390, 570
x = 15, 105, 195, 285

Check that these angles lie between 0 and 360.

I let you do parts j and k using a similar idea

Thank You.

Let me demo the second one...

0 < x < 360 implies that
0 < 2x < 720 and
-60 < 2x - 60 < 660

Once again, we need to look for angles of 2x - 60 within the range -60 to 660.

This is so that when converted to x, the values of x will lie within the range 0 to 360,

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cos (2x - 60) = (sqrt 3) / 2

Basic angle, alpha = positive inverse cosine [(sqrt 3) / 2]
Basic angle, alpha = 30

Since cos (2x - 60) has a positive value, 2x - 60 lies in the first or fourth quadrant.

As before, be careful here. The angle range -60 to 0 is within the fourth quadrant. A hidden angle might appear there.

2x - 60 = angles in firstor fourth quadrant

------------------------------------------------

2x - 60 can take one of these values (we reject them later if necessary)

1. Fourth quadrant, previous cycle
2. First quadrant
3. Fourth quadrant
4. First quadrant, next cycle
5. Fourth quadrant, next cycle

------------------------------------------------

The angles for 2x - 60 are

1. -alpha = -30 (see, it is once again important to go back one cycle)
2. alpha = 30
3. 360 - alpha = 330
4. 360 + alpha = 390
5. 720 - alpha = 690 (rejected, since it is out of range of -60 to 660; usually when one angle is rejected because it's too high, another angle is likely to appear from the other side, and here that "other angle" is -30)

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2x - 60 = -30, 30, 330, 390
2x = 30, 90, 390, 450
x = 15, 45, 195, 225

Check that these angles lie between 0 and 360.