Adding a css style to the main nav menu in child pages

in your functions.php file add the following code:

if ( is_page( yourpage ) ) //yourpage can be your page's id, title or even slug
    wp_enqueue_style( 'path/to/your/custom/css/file' ); //your stylesheet path
elseif( is_page( yourpage ) ) //yourpage can be your page's id, title or even slug
    wp_enqueue_style( '2nd/path/to/your/custom/css/file' ); //your stylesheet path
else
   wp_enqueue_style( '3rd/path/to/your/custom/css/file' ); //your stylesheet path

see also: is_page and is_single