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Lines  and  are tangent to a circle, as shown below.

[asy]
unitsize(4 cm);

pair A, O, P, Q, R, T, U;

P = (0,0);
U = (1,0);
T = dir(40);
O = extension(P, P + dir(20), U, U + (0,1));
A = intersectionpoint((U + 0.1*dir(63))--(U + 5*dir(63)), Circle(O,abs(O - U)));
Q = 1.5*T;
R = 1.5*U;

draw(Q--P--R);
draw(Circle(O,abs(O - U)));
draw(T--A--U);

label("$A$", A, NE);
label("$X$", P, SW);
label("$Q$", Q, NE);
label("$R$", R, E);
label("$T$", T, NW);
label("$U$", U, S);
[/asy]

If  and  then find  in degrees.

 Jul 24, 2022
 #1
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Not many people on this forum would make sense of this.

 Jul 24, 2022

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