Question

what is ( mangle tvu )? ( mangle tvu = square^circ )

Explanation:

Step1: Identify arc measure

The central angle $\angle US T = 86^\circ$, so the measure of arc $UT$ is $86^\circ$.

Step2: Apply inscribed angle theorem

An inscribed angle is half the measure of its intercepted arc. $\angle TVU$ intercepts arc $UT$.
$m\angle TVU = \frac{1}{2} \times m\overset{\frown}{UT}$
$m\angle TVU = \frac{1}{2} \times 86^\circ$

Step3: Calculate final angle

$m\angle TVU = 43^\circ$

Answer:

$43$