A2. Given are two points $A$ and $B$ and two circles, one with center $A$ passing through $B$ and one with center $B$ passing through $A$. Point $C$ lies on the second circle and on line $A B$. Point $D$ also lies on the second circle. Point $E$ lies on the first circle and on line $B D$. Given that $\angle D=57^{\circ}$.

How large is $\angle A$ in degrees?

Note, the figure below is not drawn to scale.

![](https://cdn.mathpix.com/cropped/2024_04_17_998065f2d90ec501d25cg-3.jpg?height=395&width=571&top_left_y=919&top_left_x=751)
B2. $48^{\circ}$

The angle at $D$ is equal to the angle at $C$ because triangle $C B D$ is isosceles (vertex angle $B$). Angle $D B C$ is then $180^{\circ}-2 \times 57^{\circ}=66^{\circ}$. Due to vertical angles, angle $A B E$ is also 66 degrees. Since triangle $B A E$ is isosceles (vertex angle $A$), the angle at $E$ is also 66 degrees. The angle at $A$ is then $180^{\circ}-2 \times 66^{\circ}=48^{\circ}$.

![](https://cdn.mathpix.com/cropped/2024_04_17_20b3a516711f91b2fa07g-3.jpg?height=354&width=511&top_left_y=503&top_left_x=1321)