AngularJS Example:

HTML

<div id="test" ng-app="testApp" ng-controller="test">
  <div>
    <h1>{{varible}}!</h1>
  </div>
</div>

<button id="first">i will not change angular value</button>
<button id="second">i will change angular value</button>

CSS

</style> <!-- Ugly Hack due to jsFiddle issue: http://goo.gl/BUfGZ --> 
<link rel="stylesheet" href="http://netdna.bootstrapcdn.com/twitter-bootstrap/2.0.4/css/bootstrap-combined.min.css">
<script src="https://ajax.googleapis.com/ajax/libs/angularjs/1.3.8/angular.min.js"></script>
<style>

JavaScript

angular.module('testApp',[]).controller('test',function($scope){
    $scope.varible = "First Value"
});


$(document).ready(function(){
    $('#first').click(function(){
        var scope = angular.element('#test').scope();
        scope.varible = 'SecondValue';
    });
    
    $('#second').click(function(){
        var scope = angular.element('#test').scope();
        scope.$apply(function () {
            scope.varible = 'SecondValue';
        });
    });
});