In a triangle, one exterior angle measures 140°. The two remote interior angles measure 3x° and (2x+10)°. What is the value of x?

The exterior angle theorem says an exterior angle equals the sum of the two remote interior angles. So $3x + (2x + 10) = 140$. Combine like terms: $5x + 10 = 140$, then $5x = 130$, and $x = 26$, choice D. Check: the angles are $78°$ and $62°$, which sum to $140°$. Choice A (28) comes from solving $5x = 140$ and forgetting the 10. Choice B (50) comes from dividing 130 incorrectly or using $140 - 90$. Choice C (14) comes from $5x + 10 = 80$ or from dropping a digit. Remember that the exterior angle equals the sum of the two non-adjacent interior angles.