Just traverse the tree forwards and backwards simultaneously and match the moves. I hate peevish interviewers. If you want to show off, write a paper.

  bool is_mirror(left_tree,right_tree) {

    if( !left_tree && !right_tree)
      return true;

    if( !left_tree || !right_tree)
      return false;

    return is_mirror(left_tree->left, right_tree->right)
      && is_mirror(left_tree->right, right_tree->left);

    }

  bool is_symmetric(tree) {
    !tree || is_mirror(tree-left,tree->right);
  }