at a meeting ,everyone shakes hands exactly once with every other person . if there are 55 handshakes . then what Is the number of people attending​

11.
Every handshake takes 2. If no one shakes hands twice with another, there are 10+1 total people shaking hands (11).

Name them 1 thru 11. Make a line and 11 goes down the line and shakes 10 hands and then leaves. 10 then shakes 9 hands and leaves. 8 then shakes 7 hands and leaves. Etc. 2 shakes hands with 1 and leaves. 1 just leaves.

11— 10 hs

10— 9 hs

9— 8 hs

8— 7 hs

7— 6 hs

6— 5 hs

5— 4 hs

4— 3 hs

3— 2 hs

2— 1 hs

1— leaves

Total handshakes 55, total people 11.