My question regards--as you might have figured--how to find a reference angle. Given in the problem is 249.3 deg. and am able to deduce that angle is found in the 3rd quadrant--but, why then am I not subtracting that from 270 deg.? So essentially my question is why do I subtract 249.3 deg. from 360 deg.?
The reference angle is always with respect to the x-axis, so you wouldn't subtract it from 270 if it's in the 3rd quandrant. It should be the difference between 180 and 249.3. In other words, the reference angle is the angle between 0 and the angle for quandrants 1 and 4, and between 180 and the angle for quandrants 2 and 3. See a pretty picture for details.
Haha, I love how you renamed the web-link--with that aside, thank you very much that clears things up.