The Givens were one side and an angle, therefore you are trying to find another side. One possibility is side AC is congruent to DF, but the angle is not in the middle so it doesn’t work. The only possible answer that can work is BC is congruent to EF
The probability of losing per flip is 1/2. Multiply 1/2 by itself 6 times since the condition is asking for the probability for the person to lose 6 times in a row. 1/2 * 1/2 * 1/2 * 1/2 * 1/2 * 1/2 = 1/64. The answer is 1/64.