Answer
In an animal with an exoskeleton, antagonistic muscles would work in the same way in the sense that they would be able to move a limb in opposite directions. However, they would be attached to an external structure, and, thus, their attachments would differ.
Work Step by Step
Here you need to see that the muscles opposing one another is a general principle, the main difference between vertebrates and arthropods being the placement of the skeleton and, thus, where muscles attach.
