The problem asks us to find the supplementary angle to a $45^\circ$ angle. Two angles are supplementary if the sum of their measures is $180^\circ$. Let $x$ be the measure of the supplementary angle.

1. Problem Description

The problem asks us to find the supplementary angle to a $45^\circ$ angle. Two angles are supplementary if the sum of their measures is $180^\circ$. Let $x$ be the measure of the supplementary angle.

2. Solution Steps

The sum of the given angle ($45^\circ$) and its supplementary angle ($x$) must be $180^\circ$. Therefore, we have the equation:

$45^\circ + x = 180^\circ$.

To solve for $x$, we subtract $45^\circ$ from both sides of the equation:

$x = 180^\circ - 45^\circ$

$x = 135^\circ$

3. Final Answer

The supplementary angle is $135^\circ$.