Step 1: Recall the classification of fibres.
Fibres are broadly classified into:
Natural fibres (obtained from plants or animals)
Synthetic fibres (man-made fibres)
Step 2: Analyze each option.
Angora: A natural fibre obtained from the hair of Angora rabbits — not synthetic Rayon: Man-made fibre derived from cellulose — synthetic (semi-synthetic) Nylon: Fully synthetic fibre
Polyester: Fully synthetic fibre
Step 3: Final conclusion.
The fibre which is not synthetic is Angora.
\[
\boxed{\text{(A)}}
\]