Excluding a single Entry ID of an Entry Type from craft.entries
You'd have to add a conditional and render the featured entry on the first paginated page only. You can access that info from the pageInfo variable.

Another thing I'd do is to remove the featured entry from the all entries criteria model by prepending the ID with 'not' in the id param (i.e. id('not 72')). You can probably reduce the amount of database queries with that change.

{# Get the featured entry #}
{% set featuredEntry = craft.entries.section('news').type('article').first() %}

{# Get all other entries #}
{% set idParam = 'not ' ~ featuredEntry.id %}
{% set entries = craft.entries.section('news').id(idParam) %}

{% paginate entries.limit(10) as pageInfo, pageEntries %}

{# Render the featured entry for the first page only #}
{% if pageInfo.currentPage == 1 %}
    {% include '/partials/_featuredArticleTemplate' with {
        entry: featuredEntry
    } %}
{% endif %}

{# Render all the other entries #}
{% for entry in pageEntries %}
    {# include partial #}
{% endfor %}