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In an isosceles triangle there are two equal angles and a different angle. Let the triangle be ABC with angle A and B same and C different. There are three possibilities:

Case-1: A = 69 B = x = 69 C = 180 - (69+69) = 180-138 = 42 So one possibility is x = 69

Case-2: A = 69 B = 69 C = x = 180 - (69+69) = 180-138 = 42 So another possibility is x = 42

Case-1: C = 69 B = x A = x So x + x + 69 = 180 ⇒ 2x = 180-69 = 111 ⇒ x = 111/2 = 55.5 So another possibility is x = 55.5

Sum of all possible values of x = 69+42+55.5 = 166.5