Solution:

\(\widehat{BOI}=\dfrac{1}{4}=\widehat{AOB}=\dfrac{1}{4}\times60^o=15^o.\)

Because OI rays are between 2 OA rays, the OB should \(\widehat{AOI}+\widehat{BOI}=\widehat{AOB}\)

Inferred \(\widehat{AOI}+15^o=60^o\) or  \(\widehat{AOI}=45^o\)To