Final answer:
Using the sum of angles in a triangle, ∠N in ∆NOP must be less than 59° and more than 0° since the sum of angles in a triangle is 180° and ∠P is 121°.
Step-by-step explanation:
The question involves solving for the unknown angle in a triangle using the Law of Sines or the sum of angles in a triangle. Given that ∆NOP has sides n = 51 cm and p = 49 cm, and an angle ∠P = 121°, we can find the possible values of ∠N using the fact that the sum of angles in a triangle equals 180°. Subtracting the known angle from 180°, we have 180° - 121° = 59° left for the sum of angles N and O. Because n > p in length, the angle opposite n (which is ∠N) must be larger than the angle opposite p (which is ∠O), thus ∠N is greater than ∠O and less than 59°. So ∠N is less than 59° and more than 0°.