Step 1: Length of minor arc AB:
$$\ell=\frac{\theta}{360^\circ}\times 2\pi r=\frac{120}{360}\times 2\times\frac{22}{7}\times 21$$
Step 2: $$\ell=\frac13\times 132=44\ \text{mm}$$
Step 3: Length of chord AB. Draw $OM\perp AB$; it bisects both AB and the angle, so $\angle AOM=60^\circ$.
$$AB=2r\sin 60^\circ=2\times 21\times\frac{\sqrt3}{2}=21\sqrt3$$
Step 4: $AB=21\times 1.73=36.33$ mm
Step 5: Perimeter of segment $=$ arc AB $+$ chord AB
$$=44+36.33=80.33\ \text{mm}$$
Answer: $80.33$ mm