smc

We set up equations to find each angle. The larger angle will be represented as $x$ and the smaller angle will be represented as $y$, in degrees. This implies that $4x=5y$ and $2\times (90-x)=90-y$ since the larger the original angle, the smaller the complement. We then find that $x=75$ and $y=60$, and their sum is $\boxed{135}$