I'll try to explain.
Your open loop gain is A, your loop gain is βA and your close loop gain is about 1/β - if βA>>1.
Now we have,
(open loop gain)÷(close loop gain)=(loop gain), that's A÷1/β=βA.
If we express above in dB:
20log(A÷1/β)=A(dB)-1/β(dB)=βA(dB) = loop gain(dB)
Now we know the loop gain is the difference between open loop gain and close loop gain on Bode plot. Then "the frequency where the open loop gain of the amplifier intercepts the closed loop gain" is where your loop gain drops to 0dB.
Let's talk about phase margin. It is defined as 180-(βA phase shift) when |βA|=1(0dB). So if we assume β is a real number, then your βA phase shift on Bode plot is same as your A(open loop gain) phase shift on Bode plot. So at the interception point we just derived above, read out your open loop phase shift, use 180 minus the phase shift, you get your answer!!!
In your case, if β=1/100, phase margin should be 90 degree.