The problem is to find the value of angle $y$, where $y$ is the exterior angle of an angle that measures $45$ degrees.

1. Problem Description

The problem is to find the value of angle $y$, where $y$ is the exterior angle of an angle that measures $45$ degrees.

2. Solution Steps

An exterior angle and its adjacent interior angle are supplementary, which means that they add up to 180 degrees.

Therefore, we have the following equation:

$y + 45 = 180$

Subtracting 45 from both sides of the equation, we have:

$y = 180 - 45$

$y = 135$

3. Final Answer

The value of angle $y$ is $135$ degrees.