we know that
The measure of the angle formed by [tex] 2 [/tex] chords that intersect inside the circle is [tex] \frac{1}{2} [/tex] the sum of the chords' intercepted arcs. (Angles of intersecting chords theorem)
so
in this problem
[tex] 63=\frac{1}{2}*(SR+TU)\\ \\ 63=\frac{1}{2}*(55+TU)\\ \\ TU=63*2-55\\ \\ TU=126-55\\ \\ TU=71 [/tex]
therefore
the answer is
The measure of the arc TU is equal to [tex] 71degrees [/tex]
