Here's the solution,
the angles made by same arc on circle's circumference are equal.
So, Angle O = Angle P
( Angles made by arc NM )
=》
[tex]5x - 37 = 3x + 1[/tex]
=》
[tex]5x - 3x = 1 + 37[/tex]
=》
[tex]2x = 38[/tex]
=》
[tex]x = 19[/tex]
now, value of angle at circumference :
=》
[tex]3x + 1[/tex]
=》
[tex](3 \times 19) + 1[/tex]
=》
[tex]57 + 1[/tex]
=》
[tex]58[/tex]
and, we know that the angle made by an arc at center is double the angle made by same arc on its circumference,
so, measure of Arc NM
=》
[tex]58 \times 2[/tex]
=》
[tex]116°[/tex]
