The problem asks us to find the size of angle $h$, given that the angle adjacent to it is $135^\circ$. We know that the angles around a point sum to $360^\circ$.

1. Problem Description

The problem asks us to find the size of angle $h$, given that the angle adjacent to it is $135^\circ$. We know that the angles around a point sum to $360^\circ$.

2. Solution Steps

We are given an angle of $135^\circ$ and need to find the remaining angle $h$ to complete the full circle. The sum of the angles around a point is $360^\circ$.

Therefore, we can write the equation:

$h + 135^\circ = 360^\circ$

To solve for $h$, we subtract $135^\circ$ from both sides of the equation:

$h = 360^\circ - 135^\circ$

$h = 225^\circ$

3. Final Answer

The size of angle $h$ is $225^\circ$.