Let C be the center of the circle. The measure of arc VSU is , so the measure of the minor arc VU is
. The central angle VCU also has measure
.
Triangle CUV is isosceles, so the angles CVU and CUV are congruent. The interior angles of any triangle are supplementary (they add to 180 degrees) so
UT is tangent to the circle, so CU is perpendicular to UT. Angles CUV and VUT are complementary, so
So finally,
degrees.
