Answer:
[tex]48^{\circ}[/tex]
Step-by-step explanation:
Consider we need to find [tex]m\widehat{FH}[/tex],
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,
[tex]m\angle ADJ = \frac{m\widehat{AJ}-m\widehat{BE}}{2}[/tex]
By the diagram,
[tex]37^{\circ}=\frac{m\widehat{AJ}-38^{\circ}}{2}[/tex]
[tex]74^{\circ}=m\widehat{AJ}-38^{\circ}[/tex]
[tex]\implies m\widehat{AJ}=74^{\circ}+38^{\circ}=112^{\circ}[/tex]
Now,
[tex]m\angle AGJ = \frac{m\widehat{AJ}-m\widehat{FH}}{2}[/tex]
[tex]32^{\circ}=\frac{112^{\circ}-m\widehat{FH}}{2}[/tex]
[tex]64^{\circ}=112^{\circ}-m\widehat{FH}[/tex]
[tex]\implies m\widehat{FH}= 112^{\circ}-64^{\circ}=48^{\circ}[/tex]
Hence, SECOND OPTION would be correct.
