jmc

If $x$ is the measure in degrees of each of the acute angles, then each of the larger angles measures $2x$ degrees. Since the number of degrees in the sum of the interior angles of an $n$-gon is $180(n-2)$, we have $$x+x+2x+2x+2x=540⟹8x=540⟹x=135/2.$$ The large angles each measure $2x=\boxed{135}$ degrees.