1. You're campaigning for an underdog political candidate in a big city. Not many people have heard of your candidate; she's obscure; she's virtually unknown. What would your story angle or peg be here? Well, why not take your candidate's weakness and turn it instead into a strength? Why not take your candidate's obscurity, her smallness, her unimportance, and make it a feature of the campaign? That would make a great story angle or peg. You'd want to say, in effect - "here we finally have a candidate that really represents the common man and woman. Look at her. She rose up from nowhere to compete in this important campaign. She's an example of how even the smallest, most inconsequential, most unheard of person can become an important force in politics for good." This is the sort of story angle or peg that you can base press releases and television, radio, newspaper, and magazine advertisements on. Remember: you want your story angle or peg to reach as many people and touch as many hearts as possible. You want to speak a universal language, as it were. Poverty, obscurity, the underdog rising to the top of the battle in victory - these are all things that everybody relates to.
2. You're starting a new business, let's say a business that helps people research their ancestry, their genealogy, where they came from. You issue a press release to announce the opening of your business; you advertise on the television and on the radio to promote your new business. Let's try to think of an effective story angle or peg in this instance. What if you were to find a person who's well-known in your community - the mayor, say - and offer her your services for free in exchange for using her story in your press release and advertisements? Everyone has an interesting ancestry if you go back far enough. This might make the perfect story angle or peg. Your press release could say, "look, we did this research for the mayor, and discovered that her ancestors came to the U.S. on the Mayflower and were the first people to start a soap and candle business upon arriving." Etc. etc. Your story angle or peg would be designed so as to interest other people who stumble across it. You want them to say - "I wonder what my ancestors were like; this sounds interesting; I want to do this."
3. You're the press secretary for an important businessman in your community, and one day he finds himself tangled up in a scandal. He's out jogging one morning, say, and a little dog runs up and starts yapping at his heels and trying to bite him and so he kicks it into the air and it flies for twenty feet and finally lands in a pile of stinging nettle. You've got problems here, obviously, as this businessman's press secretary, because your job (in part) is to keep his reputation shiny and unspotted and so engender good relations with the community. What would your story angle or peg be when you contacted various news stations in order to get your client's side of the story out? It had better be a good one, because the public has little tolerance for people who kick little dogs twenty feet through the air. Perhaps you would go on the offensive - perhaps you would appeal to everyone in your community who has been chased or annoyed or bitten or scared by a dog when jogging or walking etc. Your story angle or peg would say - "look, my client is really, really sorry that this has happened. He hasn't eaten or slept since, and has paid for the little doggie's medical bills. But really, shouldn't dog owners be responsible for their pets? Shouldn't dogs be kept in their yards and thereby prevent the possibility of their attacking little children and innocent joggers?" And so forth. Sometimes finding a story angle or peg is hard to do when it comes to public relations, but by using your brains and creativity you can come up with a lot.

For more on story angles or pegs, check out these great websites:
http://101publicrelations.com/media.html
http://101publicrelations.com/businesspromotion.html