The problem is to find the value of angle $y$, where $y$ is the obtuse angle formed by two lines, and the acute angle between the two lines is given as $45^{\circ}$.

1. Problem Description

The problem is to find the value of angle $y$, where $y$ is the obtuse angle formed by two lines, and the acute angle between the two lines is given as $45^{\circ}$.

2. Solution Steps

The sum of angles on a straight line is $180^{\circ}$. In this case, we have two angles formed by the intersection of two lines. One is the acute angle of $45^{\circ}$, and the other is the obtuse angle $y$. The sum of these two angles is $180^{\circ}$.

$y + 45^{\circ} = 180^{\circ}$

To find the value of $y$, we subtract $45^{\circ}$ from both sides of the equation:

$y = 180^{\circ} - 45^{\circ}$

$y = 135^{\circ}$

3. Final Answer

$y = 135^{\circ}$