Calculate the Sum of Angles Alpha and Beta in Perpendicular Lines

To solve this problem, we must identify the configuration shown in the diagram, which involves a right triangle. The key to resolving this problem is recognizing the geometric properties of the triangle presented:

1. In a right triangle, the sum of the two non-right angles must equal $90^\circ$. This is a fundamental property of right triangles where one angle is $90^\circ$.

2. Given that the problem involves angles $\alpha$ and $\beta$ positioned as they are in the right triangle's context, we observe that the angle at $O$, formed by the two arms making the right angle, is $90^\circ$. Note: the vertex $O$ is presented as the intersection of the vertical and horizontal directions.

3. Thus, $\alpha$ and $\beta$ are the acute angles of a right triangle:

4. Since the sum of the angles in any triangle must equal $180^\circ$, and one of these angles is the right angle, the remaining two must sum to $90^\circ$.

Therefore, the size of the angle $\alpha + \beta$ is precisely $90^\circ$.

Thus, the solution to this problem is $\alpha + \beta = 90$ degrees.