Edit in JSFiddle

var app = angular.module('myApp', []);
app.controller('myCtrl', ['$scope', '$compile', function($scope, $compile) {
	$scope.textOfDOM = 'Text show successfully';

  $scope.addDOM = function() {
    var DOMToAdd = $('<p>{{textOfDOM}}</p>');
    
    //Wrong code -- start
    //$('#DOMWrapper').append(DOMToAdd);
    //Wrong code -- end
    
    //Right code -- start
    var linkOfDOMToAdd = $compile(DOMToAdd);
    var nodeOfCompiledDOM = linkOfDOMToAdd($scope);
    $('#DOMWrapper').append(nodeOfCompiledDOM);
    //Right code -- end
  };
}]);

<div ng-app="myApp">
  <div id='DOMWrapper' ng-controller="myCtrl">
    <button ng-click='addDOM()'>Add DOM</button>
  </div>
</div>