Question

Hình 27 cho biết tia OI nằm giữa hai tia OA, OB, \(\widehat{AOB}=60^0;\widehat{BOI}=\dfrac{1}{4}\widehat{AOB}\)

Tính \(\widehat{BOI},\widehat{AOI}\) ?

Answer 1

Giải

Do tia OI nằm giũa hai tia OA, OB nên

Suy ra hay

Answer 2

\(\widehat{BOI}\) = \(\dfrac{1}{4}\) \(\widehat{AOB}\) ⇒ \(\dfrac{1}{4}\).60^o = 15^o

Vì tia OI nằm giữa 2 tia OA; OB nên:

\(\widehat{AOI}\)+ \(\widehat{IOB}\)= \(\widehat{AOB}\)

⇒ \(\widehat{AOI}\)= \(\widehat{AOB} - \widehat{IOB}\) = 60^o - 15^o = 45^o

Vậy: \(\widehat{AOI}\) = 45^o