The angle at the center is 50^. The angle at the circumference subtended by the same arc is half the angle at the center.

Here are the values of the angles: a) Step 1: The angle at the center is 50^. The angle at the circumference subtended by the same arc is half the angle at the center. a = (1)/(2) × 50^ a = 25^ a = 25^ b) Step 1: The angle at the center is 120^. The angle at the circumference subtended by the same arc is half the angle at the center. b = (1)/(2) × 120^ b = 60^ b = 60^ c) Step 1: The angle at the center is 140^. The angle at the circumference subtended by the same arc is half the angle at the center. c = (1)/(2) × 140^ c = 70^ c = 70^ d) Step 1: The angle at the center is 180^ (a straight line). The angle at the circumference subtended by the same arc is half the angle at the center. d = (1)/(2) × 180^ d = 90^ d = 90^ e) Step 1: The angle at the circumference is 30^. The angle at the center subtended by the same arc is twice the angle at the circumference. e = 2 × 30^ e = 60^ e = 60^ f) Step 1: The angle at the circumference is 35^. The angle at the center subtended by the same arc is twice the angle at the circumference. f = 2 × 35^ f = 70^ f = 70^ g) Step 1: Angles in the same segment are equal. Angle g is subtended by the same arc as the 35^ angle at the circumference. g = 35^ g = 35^ h) Step 1: The angle at the circumference is 25^. The angle at the center subtended by the same arc is twice the angle at the circumference. h = 2 × 25^ h = 50^ h = 50^ i) Step 1: Angles in the same segment are equal. Angle i is subtended by the same arc as the 25^ angle at the circumference. i = 25^ i = 25^ j) Step 1: The angle at the circumference is 26^. The angle at the center subtended by the same arc is twice the angle at the circumference. j = 2 × 26^ j = 52^ j = 52^ k) Step 1: Angles in the same segment are equal. Angle k is subtended by the same arc as the 26^ angle at the circumference. k = 26^ k = 26^ l) Step 1: The angle at the center is 140^. The angle at the circumference subtended by the same arc is half the angle at the center. l = (1)/(2) × 140^ l = 70^ l = 70^ m) Step 1: The angle at the center is 140^. The angle at the circumference subtended by the same arc is half the angle at the center. m = (1)/(2) × 140^ m = 70^ m = 70^ n) Step 1: Angles in the same segment are equal. Angle n is subtended by the same arc as angles l and m. n = 70^ n = 70^ p) Step 1: The angle at the center is 130^. The angle at the circumference subtended by the same arc is half the angle at the center. p = (1)/(2) × 130^ p = 65^ p = 65^ q) Step 1: Angles in the same segment are equal. Angle q is subtended by the same arc as angle p. q = 65^ q = 65^ r) Step 1: Angles in the same segment are equal. Angle r is subtended by the same arc as angle p. r = 65^ r = 65^ s) Step 1: The angle at the center is 100^. The angle at the circumference subtended by the same arc is half the angle at the center. s = (1)/(2) × 100^ s = 50^ s = 50^ t) Step 1: The angle at the center is 100^. The angle at the circumference subtended by the same arc is half the angle at the center. t = (1)/(2) × 100^ t = 50^ t = 50^ u) Step 1: Angles in the same segment are equal. Angle u is subtended by the same arc as angles s and t. u = 50^ u = 50^ v) Step 1: The angle at the center is 160^. The angle at the circumference subtended by the same arc is half the angle at the center. v = (1)/(2) × 160^ v = 80^ v = 80^ w) Step 1: The angle at the circumference is 40^. The angle at the center subtended by the same arc is twice the angle at the circumference. w = 2 × 40^ w = 80^ w = 80^ x) Step 1: The angle at the center is 140^. The angle at the circumference subtended by the same arc is half the angle at the center. x = (1)/(2) × 140^ x = 70^ x = 70^ y) Step 1: The angle at the center is 140^. The angle at the circumference subtended by the same arc is half the angle at the center. y = (1)/(2) × 140^ y = 70^ y = 70^ z) Step 1: The angle at the center is 80^. The angle at the circumference subtended by the same arc is half the angle at the center. z = (1)/(2) × 80^ z = 4