We are given an angle of $45^{\circ}$ formed by a line and another ray. We are asked to find the angle $P$ formed between the ray and the extension of the line.

1. Problem Description

We are given an angle of $45^{\circ}$ formed by a line and another ray. We are asked to find the angle $P$ formed between the ray and the extension of the line.

2. Solution Steps

The line forms a straight angle, which is $180^{\circ}$. The angle formed by the given ray and the line is $45^{\circ}$. The angle $P$ is the supplement to this $45^{\circ}$ angle. Therefore, we can calculate angle $P$ by subtracting $45^{\circ}$ from $180^{\circ}$.

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

$P = 135^{\circ}$

3. Final Answer

$135^{\circ}$