The problem asks for the sum of two angles: one complementary to $15^\circ$ and another supplementary to $125^\circ$. We need to find these two angles first and then add them.

Finding the Complementary Angle

A complementary angle is an angle that, when added to another angle, sums up to $90^\circ$. Let the complementary angle to $15^\circ$ be $x$. Then, the equation is:

$ x + 15^\circ = 90^\circ $

Solving for $x$:

$ x = 90^\circ - 15^\circ $

$ x = 75^\circ $

So, the angle complementary to $15^\circ$ is $75^\circ$.

Finding the Supplementary Angle

A supplementary angle is an angle that, when added to another angle, sums up to $180^\circ$. Let the supplementary angle to $125^\circ$ be $y$. Then, the equation is:

$ y + 125^\circ = 180^\circ $

Solving for $y$:

$ y = 180^\circ - 125^\circ $

$ y = 55^\circ $

So, the angle supplementary to $125^\circ$ is $55^\circ$.

Calculating the Sum

The question asks for the sum of the complementary angle ($75^\circ$) and the supplementary angle ($55^\circ$).

Sum = $75^\circ + 55^\circ$

Sum = $130^\circ$

Therefore, the sum of the angle complementary to $15^\circ$ and the angle supplementary to $125^\circ$ is $130^\circ$.