Using vertical angles, angle 1 and 3 equal each other. Therefore, x=80/4. Then, by using the sum of angle 1 and 3, 160, and using vertical angles again, we can find angle 2, which is (360-160)/2.
Okay so what you want to do is divide 888 by 6, because she stayed for 6 nights and that's the amount overall. 888 divided by 6 is 148, so she payed $148 per night. Hope this helped :)