A2. Polona wants to draw three lines that intersect at the same point (see figure), such that the angles between them satisfy $\beta=2 \alpha$ and $\alpha=3 \gamma$. How many degrees must the angle $\alpha$ be?
(A) 18
(B) 36
(C) 50
(D) 54
(E) 60
A2. If we complete the image by also marking the supplementary angles of $\alpha, \beta$, and $\gamma$, we observe that $2 \alpha + 2 \beta + 2 \gamma = 360^{\circ}$. Since $\alpha = 3 \gamma$ and $\beta = 6 \gamma$, it follows from the previous equation that $20 \gamma = 360^{\circ}$ or $\gamma = 18^{\circ}$. Therefore, $\alpha = 54^{\circ}$.