If an angle is 3150′, what is its radian measure?

Correct answer: 7π/24

The governing conversion facts are 60 angular minutes = 1 degree and 180° = π radians. First convert 3150′ into degrees: 3150 ÷ 60 = 52.5° = 105/2°. Next convert degrees to radians by multiplying by π/180. Thus the radian measure is (105/2) × (π/180) = 105π/360. Dividing numerator and denominator by 15 gives 7π/24. Therefore option B is correct. A useful check is that 3150′ is 52.5°, which is slightly less than 60°, so its radian value should be slightly less than π/3; 7π/24 is indeed 0.2917π, while the other choices represent different degree measures. The prime symbol denotes angular minutes, not ordinary length units.