I assumed that you are struggling with nested ng-repeat. Hope the following code will help you.
<!DOCTYPE html>
<html>
<script src="http://ajax.googleapis.com/ajax/libs/angularjs/1.4.8/angular.min.js"></script>
<body>
<div ng-app="myApp" ng-controller="myCtrl">
<div ng-repeat="item in artType">
<select ng-model="ddlArtType">
<option value="" disabled selected> </option>
<option ng-repeat="selectedArtType in artCultureDependencyMap[item] track by $index">
{{selectedArtType}}
</option>
</select>
</div>
</div>
<script>
var app = angular.module('myApp', []);
app.controller('myCtrl', function($scope) {
$scope.artType=['Film', 'Music', 'Sports'];
$scope.artCultureDependencyMap = {};
$scope.artCultureDependencyMap['Film'] = ['Film1', 'Film2', 'Film3'];
$scope.artCultureDependencyMap['Music'] = ['Music1', 'Music2', 'Music3'];
$scope.artCultureDependencyMap['Sports'] = ['Sports1', 'Sports2', 'Sports3'];
});
</script>
</body>
</html>