Enqueue child and parent style from the WordPress.org theme 'Responsive'

gistfile1.php

<?php

class Responsive_Childtheme_Enqueue {
  public function __construct() {
		add_action( 'wp_enqueue_scripts', array( $this, 'wp_enqueue_scripts' ) );
	}

	public function wp_enqueue_scripts() {
		wp_deregister_style( 'responsive-style' );
		wp_register_style( 'responsive-style', get_template_directory_uri() . '/style.css', false, get_responsive_template_version() );
		wp_enqueue_style( 'responsive-style' );

		wp_register_style( 'responsive-child', get_stylesheet_uri(), false, get_responsive_theme_version() );
		wp_enqueue_style( 'responsive-child' );
	}
}