Two tangent segments are drawn from an external point to a circle, forming an angle of 50° between them. What is the measure of the far…

The angle formed by two tangents from an outside point equals half the difference of the intercepted arcs: $50^\circ=\frac{\text{far}-\text{near}}{2}$, so far $-$ near $=100^\circ$. The two arcs make the full circle, so far $+$ near $=360^\circ$. Adding the two equations gives $2(\text{far})=460^\circ$, so the far arc is $230^\circ$, choice C. The near arc is $130^\circ$, which is choice A, the minor arc rather than the far one asked for. Choice B ($180^\circ$) assumes a semicircle. Choice D ($310^\circ$) is $360^\circ-50^\circ$, which wrongly equates the arc with the angle.