The midpoint of three edges of a cube are connected, as shown below.  Find $\angle XYZ,$ in degrees

[asy]
unitsize(1.2 cm);

pair A, B, C, D, T, X, Y, Z;
pair x, y, z;

x = (2,-0.2);
y = (1.2,0.8);
z = (0,2);

X = (0,0);
Y = x;
T = y;
A = z;
Z = x + y;
B = x + z;
D = y + z;
C = x + y + z;

draw((C + D)/2--(B + C)/2--(B + Y)/2,red);
draw(X--Y--Z--C--D--A--cycle);
draw(B--A);
draw(B--C);
draw(B--Y);
draw(T--X,dashed);
draw(T--D,dashed);
draw(T--Z,dashed);

label("$X$", (C + D)/2, N);
label("$Y$", (B + C)/2, SE);
label("$Z$", (B + Y)/2, W);
[/asy]
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
The midpoint of three edges of a cube are connected, as shown below.  Find $\angle XYZ,$ in degrees

[asy]
unitsize(1.2 cm);

pair A, B, C, D, T, X, Y, Z;
pair x, y, z;

x = (2,-0.2);
y = (1.2,0.8);
z = (0,2);

X = (0,0);
Y = x;
T = y;
A = z;
Z = x + y;
B = x + z;
D = y + z;
C = x + y + z;

draw((C + D)/2--(B + C)/2--(B + Y)/2,red);
draw(X--Y--Z--C--D--A--cycle);
draw(B--A);
draw(B--C);
draw(B--Y);
draw(T--X,dashed);
draw(T--D,dashed);
draw(T--Z,dashed);

label("$X$", (C + D)/2, N);
label("$Y$", (B + C)/2, SE);
label("$Z$", (B + Y)/2, W);
[/asy]
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
120^\circ
The midpoint of three edges of a cube are connected, as shown below.  Find $\angle XYZ,$ in degrees

[asy]
unitsize(1.2 cm);

pair A, B, C, D, T, X, Y, Z;
pair x, y, z;

x = (2,-0.2);
y = (1.2,0.8);
z = (0,2);

X = (0,0);
Y = x;
T = y;
A = z;
Z = x + y;
B = x + z;
D = y + z;
C = x + y + z;

draw((C + D)/2--(B + C)/2--(B + Y)/2,red);
draw(X--Y--Z--C--D--A--cycle);
draw(B--A);
draw(B--C);
draw(B--Y);
draw(T--X,dashed);
draw(T--D,dashed);
draw(T--Z,dashed);

label("$X$", (C + D)/2, N);
label("$Y$", (B + C)/2, SE);
label("$Z$", (B + Y)/2, W);
[/asy]
train