It would help if you gave some definitions, but I'll do that, hopefully correctly interpreting your question.
Define the curve as C = [xv,yv] where xv and yv are a vector of corresponding points of the curve. Then the red X can be defined as
X = [xv(1),yv(end)]; % this may not work for the general case, but
%should work for the curve you've shown if the curve starts at the left
%and moves to the right.
v1 = (X-C(1,:)); %vector to starting point of the curve
v2 = (X-C(end,:)); %vector to ending point of the curve
Cangle = acos(dot(v1,v2)/(abs(v1)*abs(v2))); % curve angle
r1 = abs(v1); % distance to starting point of curve
r2 = abs(v2); % distance to ending point of curve
