1. The problem asks for the size of angle $a$ in the triangle formed by points $A$, $B$, and $C$ on the circle. 2. Since points $A$, $B$, and $C$ lie on a circle, the triangle $ABC$ is inscribed in the circle. 3. The angle $a$ at point $B$ is an inscribed angle subtending the arc $AC$. 4. The measure of an inscribed angle is half the measure of the arc it intercepts. 5. To find $a$, we need the measure of the arc $AC$. 6. Given the options for $\theta$ are 60°, 45°, 30°, and 15°, and $a$ is marked at $B$, it is likely that $a = \theta$. 7. Therefore, the size of angle $a$ is $\boxed{15^\circ}$, assuming $\theta = 15^\circ$ as the angle marked at $B$ inside the triangle. 8. If more information is given about the arcs or other angles, the answer could be refined, but with the current data, $a = 15^\circ$.