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<div ng-app="Example">
    
    <div ng-controller="TestController">
        
        <ul>
            <li ng-repeat="item in list">
                <span>{{item.name}}</span>
                <button ng-click="add(item)">Add</button>
                <ul ng-show="item.children">
                    <li ng-repeat="child in item.children">
                        <span>{{child.name}}</span>
                    </li>
                </ul>
            </li>
        </ul>
        
    </div>
    
</div>

angular.module('Example', []).controller('TestController', [
    '$scope', 
    function ($scope) {
        $scope.list = [
            { name : 'Example 1' },
            { name : 'Example 2' },
            { name : 'Example 3' }
        ];
      
        $scope.add = function (item) {
            item.children = (item.children || []);
            var count = item.children.length + 1;
            item.children.push({
                name : 'Child ' + count
            })
        };
    }
]);