Answer:
c) 118°
Step-by-step explanation:
PN is the diameter of the given circle.
[tex] \purple {\bold {\therefore m(\widehat{PMN}) = 180°}}.... (1)\\[/tex]
Now, by inscribed angle theorem:
[tex] m\widehat {MN} = 2\times m\angle MPN\\
\therefore m\widehat {MN} = 2\times 31°\\
\red{\bold {\therefore m(\widehat {MN}) = 62°}}....(2) \\\\[/tex]
Now,
[tex] \because m(\widehat{MP}) + m(\widehat{MN}) =m(\widehat{PMN})\\
\therefore m(\widehat{MP}) + 62° =180°\\
\therefore m(\widehat{MP}) =180°-62°\\
\huge \orange {\boxed {\therefore m(\widehat{MP}) =118°}} \\[/tex]
