7. In the ellipse $\frac{x^{2}}{25}+\frac{y^{2}}{9}=1$, $F$ is the left focus, point $C$ is a point on the left directrix, a line $l$ through point $C$ intersects the ellipse at points $A, B$, connect $F A, F B, F C$, and $\angle F A B=50^{\circ}, \angle F B A=20^{\circ}$, then $\angle F C A=$ $\qquad$ .
7. $15^{\circ}$ Detailed Explanation: Draw perpendiculars from points $A$ and $B$ to the left directrix, and use the second definition to prove that $|C A| = |F A|$, which shows that $F C$ is the external angle bisector of $\angle A F B$. Therefore, $\angle C F A = \frac{1}{2}(50^{\circ} + 20^{\circ}) = 35^{\circ}$, then $\angle F C A = 50^{\circ} - 35^{\circ} = 15^{\circ}$.