Two sound waves of the same frequency and amplitude are broadcast from speakers at opposite ends of a theater. in the middle of the theater, you hear no sound. which of the following is true

the two waves are in phase in the middle of the theater.

the two waves are 45° out of phase in the middle of the theater.

the two waves are 90° out of phase in the middle of the theater.

the two waves are 180° out of phase in the middle of the theater.

The last one is true.
Lets say that wave 1 has function of W1 = A*sin(w*t) and second one 
W2 = A*(w*t - 180)
both waves have same amplitude A and same frequency (w=2*pi*f)

in t=0 first wave has value of 0 and second one has value of 0. Their sum is equal to 0.
As the time starts passing first wave's value will grow while second one will decrease and go negative (because of the shape of sinus function). Both of them are changing their value at same rate because of same frequency and their sum will always be 0. Check the graph.