Segments rt and su are diameters of circle o. what is m of srt? 258° 266° 274° 282°

The measure of ∠ROU is 94°.  That is a central angle, which means that the arc it intercepts also measures 94°.  Because ∠SOT is vertical to ∠ROU it is also a 94° angle with a 94° intercepted arc.  The other 2 angles, ∠SOR and ∠TOU are vertical and have the same measure, both the angles and their intercepted arcs.  Those measures will split the difference of 360-94-94, which is 172.  172/2 is 86.  That means that those arcs also measure 86.  Arc SRT is the addition of arc SR, RU. and UT, which are 86+94+86, respectively, which add up to 266.  Second choice down.