The points M and N are taken on the circumference on opposite sides of the diameter AB. It is known that ∠NBA = 47 °. Find the angle of the NMB.

The ANB arc is equal to the AMB arc, and both are equal to 180 °, because AB is the diameter.
∠NBA is an angle inscribed in a circle, therefore (by the inscribed angle theorem) the arc AN is 47 ° * 2 = 94 °.
Then the arc NB is 180 ° -94 ° = 86 °
∠NMB is also inscribed in a circle, therefore it is 86 ° / 2 = 43 °
Answer: 43

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