By the inscribed angle theorem, we have
[tex]m\angle C=\dfrac12m\angle AMB=\dfrac12m\widehat{AB}[/tex]
(where [tex]\widehat{AB}[/tex] denotes the minor arc AB)
[tex]\implies m\angle C=\dfrac{86^\circ}2=43^\circ[/tex]
The interior angles of any triangle sum to 180º in measure, so
[tex]m\angle A+m\angle B+m\angle C=180^\circ\implies m\angle B=86^\circ[/tex]
Use the inscribed angle theorem again to find the measure of arc BC:
[tex]m\angle A=\dfrac12m\angle BMC=\dfrac12m\widehat{BC}[/tex]
[tex]\implies m\widehat{BC}=2\cdot51^\circ=102^\circ[/tex]
Similarly find the measure of arc AC:
[tex]m\angle B=\dfrac12m\widehat{AC}[/tex]
[tex]\implies m\widehat{AC}=2\cdot86^\circ=172^\circ[/tex]
