The correct answer is $\boxed{\text{B}}$.
The altitude of a star is the angle between the horizon and the star. The declination of a star is the angle between the star’s celestial equator and the observer’s horizon. A circumpolar star is a star that never sets or rises for an observer at a given latitude.
At culmination, a star is at its highest point in the sky. For a circumpolar star, the altitude of the star at culmination is equal to the star’s declination. In this case, the altitudes of the star at culmination are 70° and 10°, so the declination of the star is $\boxed{70^\circ}$.
Option A is incorrect because 80° is greater than the declination of the star. Option C is incorrect because 60° is less
than the declination of the star. Option D is incorrect because 50° is much less than the declination of the star.