Magento: How to check if has access to page?

Syntax:

Mage::getSingleton('admin/session')
->isAllowed('[resource_item1_path]/[resource_item1_child_path]')

Example:

$adminSession = Mage::getSingleton('admin/session');
// Checks the permission for managing of products
$adminSession->isAllowed('admin/catalog/products');

// Checks the permission for the order creation in Magento Admin
$adminSession->isAllowed('sales/order/create');

// Checks the permission for the order view in Magento Admin
$adminSession->isAllowed('sales/order/view'));

Reference:
Defining acl resources custom and admin menu