How can I use the $index inside a ng-repeat to enable a class and show a DIV?

The issue here is that ng-repeat creates its own scope, so when you do selected=$index it creates a new a selected property in that scope rather than altering the existing one. To fix this you have two options:

Change the selected property to a non-primitive (ie object or array, which makes javascript look up the prototype chain) then set a value on that:

$scope.selected = {value: 0};

<a ng-click="selected.value = $index">A{{$index}}</a>

See plunker

or

Use the $parent variable to access the correct property. Though less recommended as it increases coupling between scopes

<a ng-click="$parent.selected = $index">A{{$index}}</a>

See plunker