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

Answer:

$48^{\circ}$

Step-by-step 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.