If m∠LMN is 48° in the inscribed triangle, then m∠NLM is 42°, and the correct answer is B.
In a circle with diameter LM, if triangle NLM is inscribed and the midpoint of the circle is P, forming a right triangle LMP, the angle at the center (L) is twice the angle at the circumference (N). Given m∠LMN = 48°, m∠L is twice that, making it 96°.
However, since LM is the diameter, angle LMP is a right angle, and the sum of angles in a triangle is 180°. Therefore, m∠NLM can be found by subtracting the sum of the known angles from 180°:
m∠NLM = 180° - m∠LMN - m∠LMP
m∠NLM = 180° - 48° - 90°
m∠NLM = 42°
So, the correct answer is option B, 42°, for m∠NLM.