Points M and N are taken on the circle on opposite sides of the diameter AB. Known for NBA angle = 32 ° Find angle NMB.

No matter how the points M and N are located, whether the segment MN passes through the center of the circle or not, the triangle NOВ is central, and the angle NMB is inscribed, based on the same arc.
This means that NMB = ½ * NOB.
Find the angle value NOB.
To do this, consider the triangle NOB – isosceles, since the sides NO = BO = r is the radius of the circle.
Therefore angle ONB = angle NBO = angle NBA = 32 ° and angle NOB = 180º – 2 * 32º = 116º.
Thus, the angle NMB = ½ * NOB = ½ * 116º = 58º.