Question

Please answer this question now

Answer 1

76 degrees.

Explanation:

Let as consider O is the center of the circle . So from the figure it is clear that

`\angle AOB=44^(\circ)`

`\angle COD=118^(\circ)`

By central angle theorem, central angle subtended by an arc is twice of inscribed angle of the same arc.

We know that,
`\angle BAD=97^(\circ)` and angle BOD is the central angle subtended by arc BD.

`\angle BOD=2* \angle BAD`

`\angle BOD=2* 97^(\circ)`

`\angle BOD=194^(\circ)`

Now,

`\angle BOD=\angle BOC+\angle COD`

`194^(\circ)=\angle BOC+118^(\circ)`

`194^(\circ)-118^(\circ)=\angle BOC`

`76^(\circ)=\angle BOC`

`m(arc(BC))=76^(\circ)`

Therefore, the measure of arc BC is 76 degrees.