I had a *much* more complicated way of working this out, involving advanced trigonometry and lots of other horrible stuff, but while I was typing it up I suddenly realised there was a far easier way, so that's why I'm a bit delayed.

Start by extending the bottom of the triangle towards the red line to make a bigger, right-angled triangle. Then take away the triangle that contains the angle that you want, leaving you a smaller right-angled triangle. We know that the left side of this is 210m, because we are told that part of this is 120m and the rest of it is 90m, and we know that its bottom side is 70m, because looking at the measurements of 30 and 90 tell you that the hypotenuse goes up 3 times as much as it goes across.

Using trigonometry, we can work out that the angle next to your wanted angle is tan^-1(210/70), which is ∼71.6°. As angles on a straight line add up to 180°, the final step is to take 71.6° from 180° to give your answer: **∼108.4°.**

If you want the exact answer, it's 180- tan^-1(3).

I'm interested in your other problem too, but I'm a bit exhausted after doing this one so I'll do it later.

P.S. To MathsIsFun, can you add little -1 to the list of symbols?