Find Angle α in Intersecting Lines with β = 65°: Geometry Problem

To solve this problem, let's identify the angle relationships based on the given information:

Step 1: From the diagram, angle $\beta$ is stated to be $65^\circ$. It is important to recognize that $\alpha$ and $\beta$ are positioned such that they form a pair of vertical angles.

Step 2: According to the vertical angle theorem, vertical angles are congruent. This means that if $\beta = 65^\circ$, then $\alpha$ must also equal $65^\circ$ because they are vertical angles created by intersecting lines.

Therefore, the size of angle $\alpha$ is $\mathbf{65^\circ}$.