24. Find x.

The angle subtended by an arc at the center is twice the angle subtended by the same arc at any point on the remaining part of the circle. Angle BOC subtends arc BC. Angle BAC subtends arc BC. Therefore, angle BOC = 2 * angle BAC. Given angle BAC = 40 degrees, angle BOC = 2 * 40 = 80 degrees. In triangle OBC, OB = OC (radii), so it's isosceles. Angle OBC = Angle OCB = (180 - 80) / 2 = 50 degrees. Angle x is the angle between the radius OA and the chord AB. Since AC is tangent at A, OA is perpendicular to AC. Angle OAC = 90 degrees. Angle BAC = 40 degrees. Angle OAB = Angle OAC - Angle BAC = 90 - 40 = 50 degrees. In triangle OAB, OA = OB (radii), so it's isosceles. Angle OBA = Angle OAB = 50 degrees. Angle AOB = 180 - (50 + 50) = 80 degrees. The angle x is shown as angle OAB. Therefore, x = 50 degrees.