5) Find the value of x.

The angle subtended by an arc at the center is double the angle subtended by it at any point on the remaining part of the circle. Since AB is a chord and N is a point on the circumference, the angle AOB is subtended at the center and the angle ANB is subtended at the circumference. However, the diagram shows that NM is a diameter and AB is a chord perpendicular to NM. The angle marked as x is the angle between the radius OM and the chord AB. Since AB is bisected by NM, triangle OMA and OMB are congruent right-angled triangles. The angle subtended by arc AM at the center is angle AOM. The angle subtended by arc AM at the circumference is angle ABM. The angle subtended by arc BM at the center is angle BOM. The angle subtended by arc BM at the circumference is angle BAM. Since NM is a diameter and AB is a chord perpendicular to NM, NM bisects the arc AB. Therefore, arc AM = arc MB. The central angles subtended by these arcs are equal, so angle AOM = angle BOM. Since angle AOM + angle BOM = 180 degrees (straight line NM), then angle AOM = angle BOM = 90 degrees. The angle x is indicated as the angle between OM and AB. In triangle OMB, angle OMB = 90 degrees. Angle OBM is not given. The angle x is shown as the angle between OM and the chord AB. The markings on AB indicate that it is bisected by NM. Thus, NM is perpendicular to AB. Therefore, the angle between NM and AB is 90 degrees. The angle x is shown as part of the angle subtended by arc AM at the center. Since NM is a diameter and AB is a chord perpendicular to NM, NM bisects the arc AB. Thus, arc AM = arc MB. The central angle subtended by arc AM is angle AOM. The central angle subtended by arc MB is angle BOM. Since arc AM = arc MB, then angle AOM = angle BOM. Since NM is a diameter, angle NOM = 180 degrees. Therefore, angle AOM = angle BOM = 180/2 = 90 degrees. The angle x is shown as the angle between OM and the chord AB. Since NM is perpendicular to AB, the angle between NM and AB is 90 degrees. The angle x is indicated as the angle subtended by arc AM at the center. Thus, x = 90 degrees.