If you want to delete one of your own or a reshared Google Plus App
post do the following:
(1) Select the post that you want to delete by clicking or tapping to the right of your name in the post. Do not click/tap any where else in the post, such as on a photo within the post because the delete option will not appear.
(2) As soon as you click/tap to the right of your name beside the post you want deleted, you will see that a cogwheel appears in the upper right hand corner. Click on this cogwheel, then click on: Delete Post.
Note: Deleting a Google Plus post, your own or a reshared one, is done differently then deleting a post from within the Google Plus App if you are, for example, accessing your Google Plus from within a browser or browser app. To delete a post
(1) Click or tap to the right of your name in the post (do not click any where else) then click/tap on the arrow option (looks like two upside down arrow heads) that appears in the upper right hand corner and select: Delete Post.