Here is another answer. I hope it will help.
<a class="btn" ng-click="delete(item)">Delete</a>
$scope.delete(item){
var index = this.list.indexOf(item);
this.list.splice(index, 1);
}
array.splice(start)
array.splice(start, deleteCount)
array.splice(start, deleteCount, item1, item2, ...)
Full source is here
https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/Array/splice