The two radii from Point O to the circumference of the circle are equal, as this is the definition of the radius of a circle. So, the two angles in the triangle that are not adjacent to angle m are congruent. Solving for the angle adjacent to m gives us 180-69-69 = 42 degrees. Subtracting this from 180 to solve from 180 to solve for m gives us 180-42=138 degrees. So the answer is 138 degrees.