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