In isosceles triangle $ABC$, if $BC$ is extended to a point $X$ such that $AC = CX$, what is the number of degrees in the measure of angle $AXC$? [asy] size(220);
pair B, A = B + dir(40), C = A + dir(-40), X = C + dir(0);
draw(C--A--B--X--A); draw(A/2+.1*dir(-30)--A/2-.1*dir(-30));
draw((A+C)/2+.1*dir(30)--(A+C)/2-.1*dir(30));
label("A",A,N); label("C",C,S); label("B",B,S); label("X",X,S); label("$30^{\circ}$",B+.1*dir(0),NE);
draw(arc(B,1/3,0,40));
[/asy]
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
In isosceles triangle $ABC$, if $BC$ is extended to a point $X$ such that $AC = CX$, what is the number of degrees in the measure of angle $AXC$? [asy] size(220);
pair B, A = B + dir(40), C = A + dir(-40), X = C + dir(0);
draw(C--A--B--X--A); draw(A/2+.1*dir(-30)--A/2-.1*dir(-30));
draw((A+C)/2+.1*dir(30)--(A+C)/2-.1*dir(30));
label("A",A,N); label("C",C,S); label("B",B,S); label("X",X,S); label("$30^{\circ}$",B+.1*dir(0),NE);
draw(arc(B,1/3,0,40));
[/asy]
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
15
In isosceles triangle $ABC$, if $BC$ is extended to a point $X$ such that $AC = CX$, what is the number of degrees in the measure of angle $AXC$? [asy] size(220);
pair B, A = B + dir(40), C = A + dir(-40), X = C + dir(0);
draw(C--A--B--X--A); draw(A/2+.1*dir(-30)--A/2-.1*dir(-30));
draw((A+C)/2+.1*dir(30)--(A+C)/2-.1*dir(30));
label("A",A,N); label("C",C,S); label("B",B,S); label("X",X,S); label("$30^{\circ}$",B+.1*dir(0),NE);
draw(arc(B,1/3,0,40));
[/asy]
train