Question

How to solve this problem​

Answer 1

Let C be the center of the circle. The measure of arc VSU is $2+114x$, so the measure of the minor arc VU is $360-(2+114x)=358-114x$. The central angle VCU also has measure $358-114x$.

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

$m\angle VCU+2m\angle CUV=180$

$\implies m\angle CUV=\dfrac{180-(358-114x)}2=57x-89$

UT is tangent to the circle, so CU is perpendicular to UT. Angles CUV and VUT are complementary, so

$(57x-89)+(31x+3)=90$

$\implies88x=176$

$\implies x=2$

So finally,

$m\widehat{VSU}=2+114\cdot2=230$

degrees.