In a triangle, one exterior angle measures 150°. The two remote interior angles measure 3x° and (x+30)°. What is the value of x?

By the exterior angle theorem, an exterior angle equals the sum of the two remote interior angles: $3x + (x + 30) = 150$. Combine like terms: $4x + 30 = 150$. Subtract 30: $4x = 120$. Divide: $x = 30$, choice C. Check: the angles are $90°$ and $60°$, which sum to $150°$. Choice A (40) gives angles of $120°$ and $70°$, totaling $190°$. Choice B (60) gives $180°$ and $90°$, totaling $270°$. Choice D (20) gives angles of $60°$ and $50°$, totaling $110°$. Always verify by summing the two angles.