GRE Section 2 Quantitative Exam - Question 49

Given that the radius of the circle is equal to the chord AB, triangle OAB is an isosceles triangle (OA = OB = AB). In such a triangle, the angle at the center (angle OAB) is supplementary to twice the given angle at A (which is 50 degrees) because the angle subtended by the chord at the circumference is half the angle subtended at the center of the circle for the same arc. Therefore, 2 * 50 = 100 degrees is the angle at the center. Since the total angle around point O is 360 degrees and the angle at A + angle at B (which are both equal) = supplementary to the central angle, the remaining angle at B within the triangle will also be 50 degrees as angle at A and B. Therefore, x = 50 degrees.