In measuring distaces between countries and cities. Angles are used very often to refer to a distance on the earth. Eg: If you say I've been on 360 degrees of the world, you would be saying you've been all over the world. Any show that said they report from 360 degrees would basically be saying that their show is filmed world-wide and the journalists travel all over the world to get the news they show on their show.
Also, let's say you want to make a table, but modern, not just regularly straight, but also modern and angular. You would have to know your angles to find out what angle would be best to use for the table, wouldn't you? Plus referring to angles is easier. Pretend you just got a manual for a satellite tv. How would you know in which angle to set the antennae or satellite if it didn't give a unit we knew? Or, just from a picture? It would be difficult. So, to sum up, there are so many ways we can use angles everyday!