Specify parent page template

All types of templates have filters to let you control what template is loaded. For pages there’s page_template, where you can check the queried page against an ID, or see if the ID exists in an array of a page’s ancestor IDs.

function wpd_page_template_filter( $template ){
    // the ID of Mango page
    $parent_page = 20;

    if( $parent_page == get_queried_object_id()
        || in_array( $parent_page, get_ancestors( get_queried_object_id(), 'page' ) ) ){
        $template = locate_template( 'mango.php', false );
    }
    return $template;
}
add_filter( 'page_template', 'wpd_page_template_filter' );