To determine the quadrant in which an angle of -1560 degrees lies, we first need to find its coterminal angle within the range of 0 to 360 degrees.

We can do this by adding multiples of 360 to -1560 until we get an angle in the desired range:

-1560 + 360 = -1200

-1200 + 360 = -840

-840 + 360 = -480

-480 + 360 = -120

-120 + 360 = 240

So, -1560 degrees is coterminal with 240 degrees.

Now we determine the quadrant:

• Quadrant I: 0° to 90°
• Quadrant II: 90° to 180°
• Quadrant III: 180° to 270°
• Quadrant IV: 270° to 360°

Since 240° is between 180° and 270°, the angle lies in Quadrant III.