29. Find x.

Angle MRE subtends arc ME. Angle MNE subtends arc ME. Angle MRE = Angle MNE. Angle MOE is the central angle subtending arc ME. Angle MOE = 2 * Angle MRE. Angle MRE = 30 degrees. Therefore, Angle MOE = 2 * 30 = 60 degrees. In triangle MNE, angle MEN = 180 - angle OME. Angle OME is not given. Angle MNE = 30 degrees. In triangle OEN, OE = ON (radii). Angle OEN = Angle ONE. Angle EON = 180 - Angle MOE = 180 - 60 = 120 degrees. Angle OEN = Angle ONE = (180 - 120) / 2 = 30 degrees. Angle MNE = 30 degrees. Angle ONE = 30 degrees. This means M, N, E are collinear, which is not the case. Let's re-examine. Angle MRE = 30 degrees. This is an inscribed angle subtending arc ME. The central angle subtending arc ME is angle MOE. So, angle MOE = 2 * 30 = 60 degrees. Triangle MOE is isosceles with OM = OE (radii). Since angle MOE = 60 degrees, triangle MOE is equilateral. Thus, ME = OM = OE. The radius is not given. Let's look at angle MNE. Angle MNE = x. This is an inscribed angle subtending arc ME. So, angle MOE = 2x. We are given angle OME = 30 degrees. In triangle OME, OM = OE (radii), so it's isosceles. Angle OME = Angle OEM = 30 degrees. Angle MOE = 180 - (30 + 30) = 120 degrees. Since angle MOE = 2x, 2x = 120, so x = 60 degrees. The label 30 degrees is near angle OME, not angle MRE. The label 20 is near segment RN. The label x is near segment OE. This is confusing. Let's assume x is angle MNE. Angle MRE = 30 degrees. Angle MNE = x. Both subtend arc ME. So x = 30 degrees. If x is angle OEN, then angle OEN = angle OME = 30 degrees. If x is angle OEN, and angle OME = 30 degrees, then angle MOE = 180 - 2*30 = 120 degrees. Angle MNE = 120/2 = 60 degrees. If x is angle OEN, and angle MRE = 30 degrees, then angle MOE = 60 degrees. Angle OEN = (180-60)/2 = 60 degrees. The label x is next to OE, and also next to angle MNE. Let's assume x is angle MNE. Angle MRE = 30 degrees. Both subtend arc ME. Therefore, x = 30 degrees.