Question

На окружности по разные стороны от диаметра AB взяты точки M и N. Известно, что ∠NBA=5∘. Найдите угол NMB. Ответ дайте в градусах.

Answer 1

<NBA=5°, дуга NA=2*5°=10°
дуга ANB=90° (диаметр делит окружности на 2 равные части)
дуга NB=90°-10°=80°
<NMB опирается на дугу NB, => <NMB=1/2*80°=40°

Answer 2

Problem Analysis

We are given a circle with points M and N on opposite sides of the diameter AB. It is known that angle NBA is 5 degrees. We need to find angle NMB in degrees.

Solution

To find angle NMB, we can use the fact that angles in the same segment of a circle are equal. Since angle NBA is given as 5 degrees, angle NMB will also be 5 degrees.

Therefore, the angle NMB is 5 degrees.

Conclusion

The angle NMB is 5 degrees.