Regular octagon $ABCDEFGH$ is similar to regular octagon $A^{\prime }{B}^{\prime }{C}^{\prime }{D}^{\prime }{E}^{\prime }{F}^{\prime }{G}^{\prime }{H}^{\prime }$. The length of side $A^{\prime }{B}^{\prime }$ is $2.5$ times the length of side $AB$. What is the measure of the exterior angle at vertex $D^{\prime }$?