Question

In circle C, what is m? 31° 48° 112° 121°

Answer 1

THE ANSWER IS:

the measure of the arc FH is 48 degrees

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Answer 2

`48^(\circ)`

Explanation:

Consider we need to find
`m\widehat{FH}`,

Since, if two chords of a circle intersect outside the circle then the measure of intercepted angle is half of the difference of the measures of intercepted arcs.

Thus,

`m\angle ADJ = \frac{m\widehat{AJ}-m\widehat{BE}}{2}`

By the diagram,

`37^(\circ)=\frac{m\widehat{AJ}-38^(\circ)}{2}`

`74^(\circ)=m\widehat{AJ}-38^(\circ)`

`\implies m\widehat{AJ}=74^(\circ)+38^(\circ)=112^(\circ)`

Now,

`m\angle AGJ = \frac{m\widehat{AJ}-m\widehat{FH}}{2}`

`32^(\circ)=\frac{112^(\circ)-m\widehat{FH}}{2}`

`64^(\circ)=112^(\circ)-m\widehat{FH}`

`\implies m\widehat{FH}= 112^(\circ)-64^(\circ)=48^(\circ)`

Hence, SECOND OPTION would be correct.