On a baseball diamond (which is a square with \(90\)-foot sides), the third baseman fields the ball right on the line from third base to home plate and \(10\) feet away from third base (towards home plate). When he throws the ball to first base, what angle (in degrees) does the line the ball travels make with the first base line? What angle does it make with the third base line? Draw a well-labeled diagram to support your thinking.

What angles arise if he throws the ball to second base instead?