Hey,
Right now I am about to launch an offer. It is something similar to WhatsApp, basically a messenger app.
Would you consider each one of these an angle? Free Calls, Free SMS, Free Chat ....or all they all varieties of 1 angle?
Thanks!
Basically, an angle is something you can test, which delivers results beyond doubt within a reasonable number of clicks.
Text/wording angle
Image angle
Theme angle
Cloaking angle
etc.
When your mobile ads are 5-7 words, one main word being changed is a different angle, especially if it means something different. Even if it means the same thing, the longer word could be attractive to a smarter audience.
Testing movement of image by 2px, or "the" vs "The" is not a good test as the results would take millions of clicks to be determined.
It's a grey area. Lots of good threads already here so I'd get to digging. 
Lots of different opinions will fly around as it's not a well-defined term, due to the complex nature of digital advertising.
I'll put it this way: if you have some variable you can test and have several versions of it (e.g. of ad copy, images, etc), and you could take those variations and put them into discrete categories, they likely constitute different angles.
E.g.
Ad copy:
Appeals to fear
Appeals to curiosity
Appeals to a desire of some kind
Images:
Chicks in short dresses... who are smiling
Chicks in short dresses... who are crying
Chicks in long dresses
Woman in business attire.
If it was a dating campaign... you might consider the different sets of images in these categories as being different angles, as they approach and present themselves to the user in a different way.
the angle is the copy on your banner
and the headline on your lander
I tend to think of an angle as the key benefit you're selling or pain point you're targeting.
For example, for a phone antivirus offer, angles might include "Protect your pictures", "protect your identity", "thieves could access your mobile banking", etc.
For a dating offer, it might be "women who respond to messages", "even gender balance", or just "get a girlfriend".
From there, copy, images and landers all follow.
My opinions on this are a little skewed as I'm thinking about it from a copywriting perspective, but here's my two cents:
Psychologically-speaking, whenever you're trying to get somebody to do something (this could be anything from trying to get a visitor to sign up for an offer, or trying to persuade your girlfriend to see an action movie at the theater instead of a chick flick), you're going to do it by talking about the benefits they get out of it, and trying to find one in particular that appeals to them at the current time.
Angles are simply different ways of doing that. The best direct example I can think of is pregnancy vitamins. These are vitamins pitched to women as being great for them in certain stages of pregnancy, so the women gobble them up, and it's a billion dollar industry.
In reality though, most of the time the pregnancy vitamins are just the same regular multi-vitamin that the company sells to everyone - except they repackage it as a "pregnancy" vitamin with specific benefits toward women carrying children.
So in that case, we have one product with two angles:
Product: Plain old multi-vitamin
Angle 1- One a day keeps the average person healthy.
Angle 2- Eat one a day to ensure the health of mother and baby.
The benefits are basically the same, but the angle positions them in a way that's appealing to a specific potential buyer. Human nature being what it is, #2 probably has an increased importance in the minds of most people, so I'd be willing to bet that pregnant women take vitamins a lot more diligently than regular people do.
So yes, my personal definition of angles - presenting the benefits to the end user in a way that makes it appeal specifically to them - or to a specific part of their mind. Often, if one angle doesn't work on a particular person, another angle will, even for exactly the same product.
Hope that makes sense.
2 of the best explanations of angles I've read on this forum, awesome stuff
I'm reading this thread on my kindle fire and can't find a way to give thanks to individual posts but this is a truly great thread with some gold posts. Thanks!!!!!!!
This is all SPOT on...
Going back to the OPs example:
"Would you consider each one of these an angle? Free Calls, Free SMS, Free Chat ....or all they all varieties of 1 angle?"
This can be considered 1 type of angle or multiple angles...
Personally i'd consider that 1 type of angle since it's all similar, and would consider something like "update whatsapp" a 2nd angle,
and "whatsapp now comes with new emoji's" a 3rd angle,
"get laid on whatsapp" a 4th angle
etc... 
<3 no problemo