How to manually trigger a form's submit in AngularJS?

I have a form that I wanted be nested, but it is not possible since HTML can't accept nested form. Is there a way I can manually invoke the submit(triggers the validation, e.g. required) on first form on AngularJS?

Here's how the code looks like:

<div ng-conroller="ContactController">

    <form ng-submit="saveHeaderAndDetail()">
        <label for="Description">Description</label>
        <input type="text" ng-model="Description" required/> 

        <input type="text" style="visibility:hidden" />
    </form>

    <form ng-submit="addToDetail()">
    ... 
    </form>

    <input type="button" 
        ng-click="what code could trigger the first form's submit?"/>

</div>

Btw, both forms are under one controller if that helps