Question

Find the value of MP! Need help!

Answer 1

c) 118°

Explanation:

PN is the diameter of the given circle.

`\purple {\bold {\therefore m(\widehat{PMN}) = 180°}}.... (1)\\`

Now, by inscribed angle theorem:

`m\widehat {MN} = 2* m\angle MPN\\</p><p>\therefore m\widehat {MN} = 2* 31°\\</p><p>\red{\bold {\therefore m(\widehat {MN}) = 62°}}....(2) \\\\`

Now,

`\because m(\widehat{MP}) + m(\widehat{MN}) =m(\widehat{PMN})\\</p><p>\therefore m(\widehat{MP}) + 62° =180°\\</p><p></p><p>\therefore m(\widehat{MP}) =180°-62°\\</p><p>\huge \orange {\boxed {\therefore m(\widehat{MP}) =118°}} \\`