From an external point E, tangents ES and ET are drawn to circle O. if m<E=78°, find the measure of minor arc ST.

Answer 1

Assuming you made your sketch,
angle SOT + angle E = 180° , (since the angles at S and T are each 90° )

angle SOT + 78 = 180
angle SOT = 102°

so the arc SOT = 102/360 of the circumference
= 17/60 of the circumference