Question

m\widehat{sqt}

Explanation:

Step1: Calculate the measure of the arc

The sum of the measures of arcs in a circle is \(360^{\circ}\). But we can also calculate \(m\overarc{SQT}\) by adding the measures of the arcs \(S - Q - T\).
The measure of arc \(SQ\) is \(50^{\circ}+65^{\circ}\) (from \(Q\) to \(U\) is \(65^{\circ}\) and from \(R\) to \(Q\) is \(50^{\circ}\), but wait no - actually, looking at the circle divided into central - angle - based arcs.
The measure of arc \(SQT\) is \(105^{\circ}+55^{\circ}+85^{\circ}\)

$$105 + 55+85=(105 + 55)+85=160 + 85 = 245^{\circ}$$

Answer:

\(245^{\circ}\)