On the circle on opposite sides of the diameter AB, points M and N are taken; it is known that

On the circle on opposite sides of the diameter AB, points M and N are taken; it is known that the angle NBA = 34 degrees, find the angle NMB.

In triangle ANB, the angle ANB is 90 because it is based on the diameter AB of the circle.

The sum of the interior angles of the triangle is 180.Then, in a right-angled triangle ABN, the angle BAN = 180 – ANB – ABN = 180 – 90 – 34 = 56.

The inner corner NMB rests on the arc BN and the inner corner BAN rests on the arc BN, then the angle NMB = BAN = 54.

Answer: Angle NMB = 54.