We have been given a circle. We are asked to find the measure of arc MN.
We know that the measure of all arcs in a circle is equal to 360 degrees. SO we can set an equation as:
[tex]\widehat{MN}+\widehat{NO}+\widehat{OL}+\widehat{LM}=360^{\circ}[/tex]
Upon substituting our given values, we will get:
[tex]\widehat{MN}+110^{\circ}+130^{\circ}+54^{\circ}=360^{\circ}[/tex]
[tex]\widehat{MN}+294^{\circ}=360^{\circ}[/tex]
[tex]\widehat{MN}+294^{\circ}-294^{\circ}=360^{\circ}-294^{\circ}[/tex]
[tex]\widehat{MN}=66^{\circ}[/tex]
Therefore, measure of arc MN is 66 degrees and option 'c' is the correct choice.
