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);
}