[probability] there are four people in a room that haven't met before. they are told to shake hands, exactly once, of every other person in the room so that they all meet each other. if each of these people shake their hands with every other person exactly once then how many handshakes are going to occur?

6

Step-by-step explanation:

Let the 4 people be A, B, C and D. If each of them shakes hands with another person exactly one time then that means

A shakes with B, C and D. So 3 handshakes

B already shakes with A. So B shakes with C and D. 2 handshakes

C already shakes with A and B. So C shakes with D only. 1 handshake.

D already shake hand with all above.

Total handshakes: 3 + 2 + 1 = 6

10 b/c 5*2 =10

step-by-step explanation:

second option

step-by-step explanation:

the measures of a triangle equal 180. use that to find x.

2x+3x+4x=180

9x=180

9x/9=180/9

x=20

now you know x, you know angle a is 40°, angle b is 60°, angle c is 80°.

because angle a is 40°, the first option doesn't work.

because angle b is 60°, the second option does work.

when you add angle a and b, you get 100°. complementary means it equals 90°, so the third option doesn't work.

when you add angle a and c, you get 120°, which is not 100.